diff --git a/docs/pdf/abstract.tex b/docs/pdf/abstract.tex
index 495d1885..92d0f191 100644
--- a/docs/pdf/abstract.tex
+++ b/docs/pdf/abstract.tex
@@ -1,19 +1,19 @@
-\begin{abstract}
-\emph{MLD2P4 (Multi-Level Domain Decomposition Parallel Preconditioners Package based on
-PSBLAS}) is a package of parallel algebraic multi-level preconditioners.
-It implements various versions of one-level additive and of multi-level additive
-and hybrid Schwarz algorithms. In the multi-level case, a purely algebraic approach
-is applied to generate coarse-level corrections, so that no geometric background is needed
-concerning the matrix to be preconditioned. The matrix is required to be square, real or complex, with a symmetric sparsity pattern \textbf{Non consideriamo anche il caso non simmetrico
-con $(A+A^T)/2$?}.
-
-MLD2P4 has been designed to provide scalable and easy-to-use preconditioners in the
-context of the PSBLAS (Parallel Sparse Basic Linear Algebra Subprograms)
-computational framework and can be used in conjuction with the Krylov solvers
-available in this framework. MLD2P4 enables the user to easily specify different aspects
-of a generic algebraic multilevel Schwarz preconditioner, thus allowing to search
-for the ``best'' preconditioner for the problem at hand. The package has been designed 
-employing object-oriented techniques, using Fortran 95 and MPI, with interfaces to
-additional external libraries such as UMFPACK, SuperLU and SuperLU\_Dist, that
-can be exploited in building multi-level preconditioners.
+\begin{abstract}
+\emph{MLD2P4 (Multi-Level Domain Decomposition Parallel Preconditioners Package based on
+PSBLAS}) is a package of parallel algebraic multi-level preconditioners.
+It implements various versions of one-level additive and of multi-level additive
+and hybrid Schwarz algorithms. In the multi-level case, a purely algebraic approach
+is applied to generate coarse-level corrections, so that no geometric background is needed
+concerning the matrix to be preconditioned. The matrix is required to be square, real or complex, with a symmetric sparsity pattern \textbf{Non consideriamo anche il caso non simmetrico
+con $(A+A^T)/2$?}.
+
+MLD2P4 has been designed to provide scalable and easy-to-use preconditioners in the
+context of the PSBLAS (Parallel Sparse Basic Linear Algebra Subprograms)
+computational framework and can be used in conjuction with the Krylov solvers
+available in this framework. MLD2P4 enables the user to easily specify different aspects
+of a generic algebraic multilevel Schwarz preconditioner, thus allowing to search
+for the ``best'' preconditioner for the problem at hand. The package has been designed 
+employing object-oriented techniques, using Fortran 95 and MPI, with interfaces to
+additional external libraries such as UMFPACK, SuperLU and SuperLU\_Dist, that
+can be exploited in building multi-level preconditioners.
 \end{abstract}
\ No newline at end of file
diff --git a/docs/pdf/advanced.tex b/docs/pdf/advanced.tex
index 331a2a27..d5bb941d 100644
--- a/docs/pdf/advanced.tex
+++ b/docs/pdf/advanced.tex
@@ -1,12 +1,12 @@
-\section{Advanced Use}\label{sec:advanced}
-
-    - MLD2P4 software architecture \\
-    - preconditioner data structure (descrizione "dettagliata") + possibilita' di settare singolarmente
-      i vari livelli (possibilita' accennata solamente nella precedente descrizione di precset) \\
-    - descrizione routine medium level (con introduzione sulle potenzialita' di ampliamento (?), offerte
-      da queto strato software) \\
-
-%%% Local Variables: 
-%%% mode: latex
-%%% TeX-master: "userguide"
-%%% End: 
+\section{Advanced Use}\label{sec:advanced}
+
+    - MLD2P4 software architecture \\
+    - preconditioner data structure (descrizione "dettagliata") + possibilita' di settare singolarmente
+      i vari livelli (possibilita' accennata solamente nella precedente descrizione di precset) \\
+    - descrizione routine medium level (con introduzione sulle potenzialita' di ampliamento (?), offerte
+      da queto strato software) \\
+
+%%% Local Variables: 
+%%% mode: latex
+%%% TeX-master: "userguide"
+%%% End: 
diff --git a/docs/pdf/background.tex b/docs/pdf/background.tex
index e178fde4..117f1df6 100644
--- a/docs/pdf/background.tex
+++ b/docs/pdf/background.tex
@@ -1,291 +1,291 @@
-\section{Multi-level Domain Decomposition Background\label{sec:background}}
-
-\emph{Domain Decomposition} (DD) preconditioners, coupled with Krylov iterative
-solvers, are widely used in the parallel solution of large and sparse linear systems.
-These preconditioners are based on the divide and conquer technique: the matrix
-to be preconditioned is divided into submatrices, a ``local linear system''
-involving each submatrix is (approximately) solved, and the local solutions are used
-to build a preconditioner for the whole original matrix. This process
-often corresponds to dividing a physical domain associated to the original matrix
-into subdomains, e.g. in a PDE discretization, to (approximately) solving the
-subproblems corresponding to the subdomains and to building an approximate
-solution of the original problem from the local solutions 
-\cite{Cai_Widlund_92,dd1_94,dd2_96}. 
-
-\emph{Additive Schwarz} preconditioners are DD preconditioners using overlapping
-submatrices, i.e.\ with some common rows, to couple the local information
-related to the submatrices (see, e.g., \cite{dd2_96}).
-The main motivations for choosing Additive Schwarz preconditioners are their
-intrinsic parallelism and good \textbf{(dire good e' un po' "`forte"', dato che
-subito dopo diciamo che la convergenza dipende dal numero di sottomatrici)}
-convergence properties. A drawback of these
-preconditioners is that the number of iterations of the preconditioned solvers
-generally grows with the number of submatrices. This may be a serious limitation
-on parallel computers, since the number of submatrices usually matches the number
-of available processors. Optimal convergence rates, i.e.\ iteration numbers
-independent of the number of submatrices, can be obtained by correcting the
-preconditioner through a suitable approximation of the original linear system
-in a coarse space, which globally couples the information related to the single
-submatrices. 
-
-\emph{Two-level Schwarz} preconditioners are obtained
-by combining basic (one-level) Schwarz preconditioners with coarse-level
-corrections. In this context, the one-level preconditioner is often
-called smoother. Different two-level preconditioners are obtained by varying the
-choice of the smoother, of the coarse-level correction and the
-way they are combined \cite{dd2_96}. The same reasoning can be applied starting
-from the coarse-level system, i.e.\ a coarse-space correction can be built
-from this system, thus obtaining \emph{multi-level} preconditioners.
-
-It is worth noting that optimal preconditioners do not necessarily correspond
-to minimum execution times. Indeed, to obtain effective multilevel preconditioners
-a tradeoff between optimality of convergence and the cost of building and applying
-the coarse-space corrections must be achieved. The choice of the number of levels,
-i.e.\ of the coarse-space corrections, also affects the effectiveness of the
-preconditioners. One more goal is to get convergence rates as less sensitive
-as possible to variations in the matrix coefficients.
-
-Two main approaches can be used to build coarse-space corrections. The geometric approach
-applies coarsening strategies based on the knowledge of some physical grid associated
-to the matrix and requires the user to define grid transfer operators from the fine
-to the coarse levels and vice versa. This may result difficult for complex geometries;
-furthermore, suitable one-level preconditioners may be required to get efficient
-interplay between fine and coarse levels, e.g.\ when matrices with highly varying coefficients
-are considered. The algebraic approach builds coarse-space corrections using only matrix
-information. It performs a fully automatic coarsening and enforces the interplay between
-the fine and coarse levels by suitably choosing the coarse space and the coarse-to-fine
-interpolation \cite{StubenGMD69_99}.
-
-MLD2P4 uses a pure algebraic approach for building the sequence of coarse matrices
-starting from the original matrix. The algebraic approach is based on the \emph{smoothed 
-aggregation} algorithm \cite{Brezina_Vanek_,Vanek_Mandel_Brezina_}. A decoupled version
-of this algorithm is implemented, where the smoothed aggregation is applied locally
-to each submatrix \cite{Tuminaro_Tong_00}. In the next two subsections we provide
-a brief description of the multi-level Schwarz preconditioners and on the smoothed
-aggregation technique as implemented in MLD2P4. For further details the user
-is referred to \cite{para_04,apnum_07,aaecc_07,dd2_96}.
-
-
-\subsection{Multi-level Schwarz Preconditioners\label{sec:multilevel}}
-
-The Multilevel preconditioners implemented in MLD2P4 are obtained by combining
-Additive Schwarz preconditioners with coarse-space corrections; therefore
-we first provide a sketch of the Additive Schwarz preconditioners.
-
-Given a linear system
-\[ Ax=b, \]
-where $A=(a_{ij}) \in \Re^{n \times n}$ is a
-nonsingular sparse matrix with a symmetric non-zero pattern,
-let $G=(W,E)$ be the adjacency graph of $A$, where $W=\{1, 2, \ldots, n\}$
-and $E=\{(i,j) : a_{ij} \neq 0\}$ are the vertex set and the edge set of $G$,
-respectively. Two vertices are called adjacent if there is an edge connecting
-them. For any integer $\delta > 0$, a $\delta$-overlap
-partition of $W$ can be defined recursively as follows.
-Given a 0-overlap (or non-overlapping) partition of $W$,
-i.e.\ a set of $m$ disjoint nonempty sets $W_i^0 \subset W$ such that
-$\cup_{i=1}^m W_i^0 = W$, a $\delta$-overlap
-partition of $W$ is obtained by considering the sets
-$W_i^\delta \supset W_i^{\delta-1}$, obtained by including the vertices that
-are adjacent to any vertex in $W_i^{\delta-1}$.
-
-Let $n_i^\delta$ be the size of $W_i^\delta$ and $R_i^{\delta} \in 
-\Re^{n_i^\delta \times n}$ the restriction operator that maps
-a vector $v \in \Re^n$ onto the vector $v_i^{\delta} \in \Re^{n_i^\delta}$
-containing the components of $v$ corresponding to the vertices in
-$W_i^\delta$. The transpose of $R_i^{\delta}$ is a
-prolongation operator from $\Re^{n_i^\delta}$ to $\Re^n$.
-The matrix $A_i^\delta=R_i^\delta A (R_i^\delta)^T \in
-\Re^{n_i^\delta \times n_i^\delta}$ can be considered
-as a restriction of $A$ corresponding to the set $W_i^{\delta}$.
-
-The \emph{classical one-level AS} preconditioner is defined by
-\[
-M_{AS}^{-1}= \sum_{i=1}^m (R_i^{\delta})^T 
-(A_i^\delta)^{-1} R_i^{\delta},
-\]
-where $A_i^\delta$ is assumed to be nonsingular. Its application
-to a vector $v \in \Re^n$ within a Krylov solver requires the following
-three steps:
-\begin{enumerate}
-	\item restriction of $v$ as $v_i = R_i^{\delta} v$, $i=1,\ldots,m$;
-	\item (approximate) solution of the linear systems $A_i^\delta w_i = v_i$,
-	      $i=1,\ldots,m$;
-	\item prolongation and sum of the $w_i$'s, i.e. $w = \sum_{i=1}^m (R_i^{\delta})^T w_i$.
-\end{enumerate}
-A variant of the classical AS preconditioner that outperforms it
-in terms of both convergence rate and of computation and communication
-time on parallel distributed-memory computers is the so-called \emph{Restricted AS
-(RAS)} preconditioner~\cite{Cai_Sarkis,Efstathiou_Gander}. It
-is obtained by zeroing the components of $w_i$ corresponding to the
-overlapping vertices when applying the prolongation. Therefore,
-RAS differs from classical AS by the prolongation operator $(R_i^{\delta})^T$,
-which is substituted by $(\tilde{R}_i^0)^T \in \Re^{n_i^\delta \times n}$,
-where $\tilde{R}_i^0$ obtained by zeroing the rows of $R_i^\delta$
-corresponding to the vertices in $W_i^\delta \backslash W_i^0$:
-\[
-M_{RAS}^{-1}= \sum_{i=1}^m (\tilde{R}_i^0)^T 
-(A_i^\delta)^{-1} R_i^{\delta}.
-\]
-Analogously, the AS variant called \emph{AS with Harmonic extension (ASH)}
-is defined by
-\[ M_{ASH}^{-1}= \sum_{i=1}^m (R_i^{\delta})^T 
-(A_i^\delta)^{-1} \tilde{R}_i^0.
-\]
-We note that for $\delta=0$ the three variants of the AS preconditioner are
-all equal to the block-Jacobi preconditioner.
-
-As already observed, the convergence rate of the one-level Schwarz
-preconditioned iterative solvers deteriorates as the number $m$ of partitions
-of $W$ increases \cite{dd1_94,dd2_96}. To reduce the dependency
-of the number of iterations on the degree of parallelism we may
-introduce a global coupling among the overlapping partitions by defining 
-a coarse-space approximation $A_C$ of the matrix $A$. 
-In a pure algebraic setting, $A_C$ is usually built with
-a Galerkin approach. Given a set $W_C$ of \emph{coarse vertices},
-with size $n_C$, and a suitable restriction operator
-$R_C \in \Re^{n_C \times n}$, $A_C$ is defined as
-\[
-A_C=R_C A R_C^T
-\]
-and the coarse-level correction matrix to be combined with a generic
-one-level AS preconditioner $M_{1L}$ is obtained as
-\[
-M_{C}^{-1}= R_C^T A_C^{-1} R_C,
-\]
-where $A_C$ is assumed to be nonsingular. The application of $M_{C}^{-1}$
-to a vector $v$ corresponds to a restriction, a solution and
-a prolongation step; the solution step, involving the matrix $A_C$,
-may be carried out also approximately.
-
-The combination of $M_{C}$ and $M_{1L}$ may be
-performed in either an additive or a multiplicative framework.
-In the former case, the \emph{two-level additive} Schwarz preconditioner
-is obtained:
-\[
-M_{2LA}^{-1} = M_{C}^{-1} + M_{1L}^{-1}. 
-\]
-Applying $M_{2L-A}^{-1}$ to a vector $v$ within a Krylov solver
-corresponds to applying $M_{C}^{-1}$
-and $M_{1L}^{-1}$ to $v$ independently and then summing up
-the results.
-
-In the multiplicative case, the combination can be
-performed by first applying the smoother $M_{1L}^{-1}$ and then
-the coarse-level correction operator $M_{C}^{-1}$:
-\[
-\begin{array}{l}
-w = M_{1L}^{-1} v, \\
-z = w + M_{C}^{-1} (v-Aw);
-\end{array}
-\]
-this corresponds to the following \emph{two-level hybrid pre-smoothed}
-Schwarz preconditioner:
-\[
-M_{2LH-PRE}^{-1} = M_{C}^{-1} + \left( I - M_{C}^{-1}A \right) M_{1L}^{-1}. 
-\]
-On the other hand, by applying the smoother after the coarse-level correction,
-i.e.\ by computing
-\[
-\begin{array}{l}
-w = M_{C}^{-1} v , \\
-z = w + M_{1L}^{-1} (v-Aw) , 
-\end{array}
-\]
-the \emph{two-level hybrid post-smoothed}
-Schwarz preconditioner is obtained:
-\[
-M_{2LH-POST}^{-1} = M_{1L}^{-1} + \left( I - M_{1L}^{-1}A \right) M_{C}^{-1}. 
-\]
-One more variant of two-level hybrid preconditioner is obtained by applying
-the smoother before and after the coarse-level correction. In this case, the
-preconditioner is symmetric if $A$, $M_{1L}$ and $M_{C}$ are symmetric.
-
-As previously noted, on parallel computers the number of sumatrices usually matches
-the number of available processors. When the size of the system to be preconditioned
-is very large, the use of many proccessors, i.e.\ of many small submatrices, often
-leads to a large coarse-level system, whose solution may be computationally expensive.
-On the other hand, the use of few processors often leads to local sumatrices that
-are too expensive to be processed on single processors, because of memory and/or
-computing requirements. Therefore, it seems natural to use a recursive approach,
-in which the coarse-level correction is re-applied starting from the current
-coarse-level system. The corresponding preconditioners are called \emph{multi-level}.
-One more reason for the multi-level approach is that it may significantly
-reduce the computational cost of preconditioning with respect to the two-level case
-(see \cite[Chapter 3]{dd2_96}). Additive and hybrid multilevel preconditioners
-are obtained as direct extensions of the two-level counterparts. Other combinations
-of the smoothers and coarse-level corrections are possible, leading to variants
-of the previous algorithms. For a detailed descrition of them, the reader is
-referred to \cite[Chapter 3]{dd2_96}.
-\textbf{Secondo me qui ci vorrebbe una descrizione algoritmica, a titolo di esempio,
-di un precondizionatore multilevel, ad esempio quello ibrido con pre-smoothing, sul tipo
-della descrizione in figura 1 della guida di Trilinos ML 4.0. CHE NE PENSATE?}
-
-
-\subsection{Smoothed Aggregation\label{sec:aggregation}}
-
-To define the restriction operator $R_C$, which is used to compute
-the coarse-level matrix $A_C$, MLD2P4 uses the \emph{smoothed aggregation}
-algorithm described in \cite{Brezina_Vanek_,Vanek_Mandel_Brezina_}.
-The basic idea of this algorithm is to build a coarse set of vertices
-$W_C$ by suitably grouping the vertices of $W$ into disjoint subsets
-(aggregates), and to define the coarse-to-fine space transfer operator $R_C^T$ by
-applying a suitable smoother to a simple piecewise constant
-prolongation operator, to improve the quality of the coarse-space correction.
-
-Three main steps can be identified in the smoothed aggregation procedure:
-\begin{itemize}
-	\item coarsening of the vertex set $W$, to obtain $W_C$;
-	\item construction of the prolongator $R_C^T$;
-	\item application of $R_C$ and $R_C^T$ to build $A_C$.
-\end{itemize}
- 
-To perform the coarsening step, we have implemented the aggregation algorithm sketched
-in \cite{apnum_07}. According to \cite{brezina_vanek}, a modification of this algorithm
-has been actually considered,
-in which each aggregate $N_r$ is made of vertices of $W$ that are \emph{strongly coupled}
-to a certain root vertex $r \in W$, i.e.\
-\[  N_r = \left\{s \in W: |a_{rs}| \geq \theta \sqrt{|a_{rr}a_{ss}|} \right\} \]
-for a given $\theta \in [0,1]$.
-Since the previous algorithm has a sequential nature, a \emph{decoupled} version of
-it has been chosen, where each processor $i$ independently applies the algorithm to
-the set of vertices $W_i^0$ assigned to it in the initial data distribution. This
-version is embarrassingly parallel, since it does not require any data communication.
-On the other hand, it may produce non-uniform aggregates near boundary vertices,
-i.e.\ near vertices adjacent to vertices in other processors, and is strongly
-dependent on the number of processors and on the initial partitioning of the matrix $A$.
-Nevertheless, this algorithm has been chosen for the implementation in MLD2P4,
-since it has been shown to produce good results in practice \cite{Tuminaro_Tong_00}.
-
-The prolongator $P_C=R_C^T$ is built starting from a \emph{tentative prolongator}
-$P \in \Re^{n \times n_C}$, defined as
-\begin{equation} 
-P=(p_{ij}), \quad  p_{ij}= 
-\left\{ \begin{array}{ll}
-1 & \quad \mbox{if} \; i \in V^j_C \\
-0 & \quad \mbox{otherwise}
-\end{array} \right. .
-\label{eq:tent_prol}
-\end{equation}
-$P_C$ is obtained by
-applying to $P$ a smoother $S \in \Re^{n \times n}$:
-\begin{equation}
-P_C = S P,
-\label{eq:smoothed_prol}
-\end{equation}
-in order to remove oscillatory components from the range of the prolongator
-and hence to improve the convergence properties of the multi-level
-Schwarz method \cite{Brezina_Vanek_,StubenGMD69_99}.
-A simple choice for $S$ is the damped Jacobi smoother:
-\begin{equation}
-S = I - \omega D^{-1} A , 
-\label{eq:jac_smoother}
-\end{equation}
-where the value of $\omega$ can be chosen
-using some estimate of the spectral radius of $D^{-1}A$ \cite{Brezina_Vanek}.
-\textbf{Cenno al filtering di $A$ nello smoothing, dicendo che pero' non e' stato
-implementato?}
-
-%%% Local Variables: 
-%%% mode: latex
-%%% TeX-master: "userguide"
-%%% End: 
+\section{Multi-level Domain Decomposition Background\label{sec:background}}
+
+\emph{Domain Decomposition} (DD) preconditioners, coupled with Krylov iterative
+solvers, are widely used in the parallel solution of large and sparse linear systems.
+These preconditioners are based on the divide and conquer technique: the matrix
+to be preconditioned is divided into submatrices, a ``local linear system''
+involving each submatrix is (approximately) solved, and the local solutions are used
+to build a preconditioner for the whole original matrix. This process
+often corresponds to dividing a physical domain associated to the original matrix
+into subdomains, e.g. in a PDE discretization, to (approximately) solving the
+subproblems corresponding to the subdomains and to building an approximate
+solution of the original problem from the local solutions 
+\cite{Cai_Widlund_92,dd1_94,dd2_96}. 
+
+\emph{Additive Schwarz} preconditioners are DD preconditioners using overlapping
+submatrices, i.e.\ with some common rows, to couple the local information
+related to the submatrices (see, e.g., \cite{dd2_96}).
+The main motivations for choosing Additive Schwarz preconditioners are their
+intrinsic parallelism and good \textbf{(dire good e' un po' "`forte"', dato che
+subito dopo diciamo che la convergenza dipende dal numero di sottomatrici)}
+convergence properties. A drawback of these
+preconditioners is that the number of iterations of the preconditioned solvers
+generally grows with the number of submatrices. This may be a serious limitation
+on parallel computers, since the number of submatrices usually matches the number
+of available processors. Optimal convergence rates, i.e.\ iteration numbers
+independent of the number of submatrices, can be obtained by correcting the
+preconditioner through a suitable approximation of the original linear system
+in a coarse space, which globally couples the information related to the single
+submatrices. 
+
+\emph{Two-level Schwarz} preconditioners are obtained
+by combining basic (one-level) Schwarz preconditioners with coarse-level
+corrections. In this context, the one-level preconditioner is often
+called smoother. Different two-level preconditioners are obtained by varying the
+choice of the smoother, of the coarse-level correction and the
+way they are combined \cite{dd2_96}. The same reasoning can be applied starting
+from the coarse-level system, i.e.\ a coarse-space correction can be built
+from this system, thus obtaining \emph{multi-level} preconditioners.
+
+It is worth noting that optimal preconditioners do not necessarily correspond
+to minimum execution times. Indeed, to obtain effective multilevel preconditioners
+a tradeoff between optimality of convergence and the cost of building and applying
+the coarse-space corrections must be achieved. The choice of the number of levels,
+i.e.\ of the coarse-space corrections, also affects the effectiveness of the
+preconditioners. One more goal is to get convergence rates as less sensitive
+as possible to variations in the matrix coefficients.
+
+Two main approaches can be used to build coarse-space corrections. The geometric approach
+applies coarsening strategies based on the knowledge of some physical grid associated
+to the matrix and requires the user to define grid transfer operators from the fine
+to the coarse levels and vice versa. This may result difficult for complex geometries;
+furthermore, suitable one-level preconditioners may be required to get efficient
+interplay between fine and coarse levels, e.g.\ when matrices with highly varying coefficients
+are considered. The algebraic approach builds coarse-space corrections using only matrix
+information. It performs a fully automatic coarsening and enforces the interplay between
+the fine and coarse levels by suitably choosing the coarse space and the coarse-to-fine
+interpolation \cite{StubenGMD69_99}.
+
+MLD2P4 uses a pure algebraic approach for building the sequence of coarse matrices
+starting from the original matrix. The algebraic approach is based on the \emph{smoothed 
+aggregation} algorithm \cite{Brezina_Vanek_,Vanek_Mandel_Brezina_}. A decoupled version
+of this algorithm is implemented, where the smoothed aggregation is applied locally
+to each submatrix \cite{Tuminaro_Tong_00}. In the next two subsections we provide
+a brief description of the multi-level Schwarz preconditioners and on the smoothed
+aggregation technique as implemented in MLD2P4. For further details the user
+is referred to \cite{para_04,apnum_07,aaecc_07,dd2_96}.
+
+
+\subsection{Multi-level Schwarz Preconditioners\label{sec:multilevel}}
+
+The Multilevel preconditioners implemented in MLD2P4 are obtained by combining
+Additive Schwarz preconditioners with coarse-space corrections; therefore
+we first provide a sketch of the Additive Schwarz preconditioners.
+
+Given a linear system
+\[ Ax=b, \]
+where $A=(a_{ij}) \in \Re^{n \times n}$ is a
+nonsingular sparse matrix with a symmetric non-zero pattern,
+let $G=(W,E)$ be the adjacency graph of $A$, where $W=\{1, 2, \ldots, n\}$
+and $E=\{(i,j) : a_{ij} \neq 0\}$ are the vertex set and the edge set of $G$,
+respectively. Two vertices are called adjacent if there is an edge connecting
+them. For any integer $\delta > 0$, a $\delta$-overlap
+partition of $W$ can be defined recursively as follows.
+Given a 0-overlap (or non-overlapping) partition of $W$,
+i.e.\ a set of $m$ disjoint nonempty sets $W_i^0 \subset W$ such that
+$\cup_{i=1}^m W_i^0 = W$, a $\delta$-overlap
+partition of $W$ is obtained by considering the sets
+$W_i^\delta \supset W_i^{\delta-1}$, obtained by including the vertices that
+are adjacent to any vertex in $W_i^{\delta-1}$.
+
+Let $n_i^\delta$ be the size of $W_i^\delta$ and $R_i^{\delta} \in 
+\Re^{n_i^\delta \times n}$ the restriction operator that maps
+a vector $v \in \Re^n$ onto the vector $v_i^{\delta} \in \Re^{n_i^\delta}$
+containing the components of $v$ corresponding to the vertices in
+$W_i^\delta$. The transpose of $R_i^{\delta}$ is a
+prolongation operator from $\Re^{n_i^\delta}$ to $\Re^n$.
+The matrix $A_i^\delta=R_i^\delta A (R_i^\delta)^T \in
+\Re^{n_i^\delta \times n_i^\delta}$ can be considered
+as a restriction of $A$ corresponding to the set $W_i^{\delta}$.
+
+The \emph{classical one-level AS} preconditioner is defined by
+\[
+M_{AS}^{-1}= \sum_{i=1}^m (R_i^{\delta})^T 
+(A_i^\delta)^{-1} R_i^{\delta},
+\]
+where $A_i^\delta$ is assumed to be nonsingular. Its application
+to a vector $v \in \Re^n$ within a Krylov solver requires the following
+three steps:
+\begin{enumerate}
+	\item restriction of $v$ as $v_i = R_i^{\delta} v$, $i=1,\ldots,m$;
+	\item (approximate) solution of the linear systems $A_i^\delta w_i = v_i$,
+	      $i=1,\ldots,m$;
+	\item prolongation and sum of the $w_i$'s, i.e. $w = \sum_{i=1}^m (R_i^{\delta})^T w_i$.
+\end{enumerate}
+A variant of the classical AS preconditioner that outperforms it
+in terms of both convergence rate and of computation and communication
+time on parallel distributed-memory computers is the so-called \emph{Restricted AS
+(RAS)} preconditioner~\cite{Cai_Sarkis,Efstathiou_Gander}. It
+is obtained by zeroing the components of $w_i$ corresponding to the
+overlapping vertices when applying the prolongation. Therefore,
+RAS differs from classical AS by the prolongation operator $(R_i^{\delta})^T$,
+which is substituted by $(\tilde{R}_i^0)^T \in \Re^{n_i^\delta \times n}$,
+where $\tilde{R}_i^0$ obtained by zeroing the rows of $R_i^\delta$
+corresponding to the vertices in $W_i^\delta \backslash W_i^0$:
+\[
+M_{RAS}^{-1}= \sum_{i=1}^m (\tilde{R}_i^0)^T 
+(A_i^\delta)^{-1} R_i^{\delta}.
+\]
+Analogously, the AS variant called \emph{AS with Harmonic extension (ASH)}
+is defined by
+\[ M_{ASH}^{-1}= \sum_{i=1}^m (R_i^{\delta})^T 
+(A_i^\delta)^{-1} \tilde{R}_i^0.
+\]
+We note that for $\delta=0$ the three variants of the AS preconditioner are
+all equal to the block-Jacobi preconditioner.
+
+As already observed, the convergence rate of the one-level Schwarz
+preconditioned iterative solvers deteriorates as the number $m$ of partitions
+of $W$ increases \cite{dd1_94,dd2_96}. To reduce the dependency
+of the number of iterations on the degree of parallelism we may
+introduce a global coupling among the overlapping partitions by defining 
+a coarse-space approximation $A_C$ of the matrix $A$. 
+In a pure algebraic setting, $A_C$ is usually built with
+a Galerkin approach. Given a set $W_C$ of \emph{coarse vertices},
+with size $n_C$, and a suitable restriction operator
+$R_C \in \Re^{n_C \times n}$, $A_C$ is defined as
+\[
+A_C=R_C A R_C^T
+\]
+and the coarse-level correction matrix to be combined with a generic
+one-level AS preconditioner $M_{1L}$ is obtained as
+\[
+M_{C}^{-1}= R_C^T A_C^{-1} R_C,
+\]
+where $A_C$ is assumed to be nonsingular. The application of $M_{C}^{-1}$
+to a vector $v$ corresponds to a restriction, a solution and
+a prolongation step; the solution step, involving the matrix $A_C$,
+may be carried out also approximately.
+
+The combination of $M_{C}$ and $M_{1L}$ may be
+performed in either an additive or a multiplicative framework.
+In the former case, the \emph{two-level additive} Schwarz preconditioner
+is obtained:
+\[
+M_{2LA}^{-1} = M_{C}^{-1} + M_{1L}^{-1}. 
+\]
+Applying $M_{2L-A}^{-1}$ to a vector $v$ within a Krylov solver
+corresponds to applying $M_{C}^{-1}$
+and $M_{1L}^{-1}$ to $v$ independently and then summing up
+the results.
+
+In the multiplicative case, the combination can be
+performed by first applying the smoother $M_{1L}^{-1}$ and then
+the coarse-level correction operator $M_{C}^{-1}$:
+\[
+\begin{array}{l}
+w = M_{1L}^{-1} v, \\
+z = w + M_{C}^{-1} (v-Aw);
+\end{array}
+\]
+this corresponds to the following \emph{two-level hybrid pre-smoothed}
+Schwarz preconditioner:
+\[
+M_{2LH-PRE}^{-1} = M_{C}^{-1} + \left( I - M_{C}^{-1}A \right) M_{1L}^{-1}. 
+\]
+On the other hand, by applying the smoother after the coarse-level correction,
+i.e.\ by computing
+\[
+\begin{array}{l}
+w = M_{C}^{-1} v , \\
+z = w + M_{1L}^{-1} (v-Aw) , 
+\end{array}
+\]
+the \emph{two-level hybrid post-smoothed}
+Schwarz preconditioner is obtained:
+\[
+M_{2LH-POST}^{-1} = M_{1L}^{-1} + \left( I - M_{1L}^{-1}A \right) M_{C}^{-1}. 
+\]
+One more variant of two-level hybrid preconditioner is obtained by applying
+the smoother before and after the coarse-level correction. In this case, the
+preconditioner is symmetric if $A$, $M_{1L}$ and $M_{C}$ are symmetric.
+
+As previously noted, on parallel computers the number of sumatrices usually matches
+the number of available processors. When the size of the system to be preconditioned
+is very large, the use of many proccessors, i.e.\ of many small submatrices, often
+leads to a large coarse-level system, whose solution may be computationally expensive.
+On the other hand, the use of few processors often leads to local sumatrices that
+are too expensive to be processed on single processors, because of memory and/or
+computing requirements. Therefore, it seems natural to use a recursive approach,
+in which the coarse-level correction is re-applied starting from the current
+coarse-level system. The corresponding preconditioners are called \emph{multi-level}.
+One more reason for the multi-level approach is that it may significantly
+reduce the computational cost of preconditioning with respect to the two-level case
+(see \cite[Chapter 3]{dd2_96}). Additive and hybrid multilevel preconditioners
+are obtained as direct extensions of the two-level counterparts. Other combinations
+of the smoothers and coarse-level corrections are possible, leading to variants
+of the previous algorithms. For a detailed descrition of them, the reader is
+referred to \cite[Chapter 3]{dd2_96}.
+\textbf{Secondo me qui ci vorrebbe una descrizione algoritmica, a titolo di esempio,
+di un precondizionatore multilevel, ad esempio quello ibrido con pre-smoothing, sul tipo
+della descrizione in figura 1 della guida di Trilinos ML 4.0. CHE NE PENSATE?}
+
+
+\subsection{Smoothed Aggregation\label{sec:aggregation}}
+
+To define the restriction operator $R_C$, which is used to compute
+the coarse-level matrix $A_C$, MLD2P4 uses the \emph{smoothed aggregation}
+algorithm described in \cite{Brezina_Vanek_,Vanek_Mandel_Brezina_}.
+The basic idea of this algorithm is to build a coarse set of vertices
+$W_C$ by suitably grouping the vertices of $W$ into disjoint subsets
+(aggregates), and to define the coarse-to-fine space transfer operator $R_C^T$ by
+applying a suitable smoother to a simple piecewise constant
+prolongation operator, to improve the quality of the coarse-space correction.
+
+Three main steps can be identified in the smoothed aggregation procedure:
+\begin{itemize}
+	\item coarsening of the vertex set $W$, to obtain $W_C$;
+	\item construction of the prolongator $R_C^T$;
+	\item application of $R_C$ and $R_C^T$ to build $A_C$.
+\end{itemize}
+ 
+To perform the coarsening step, we have implemented the aggregation algorithm sketched
+in \cite{apnum_07}. According to \cite{brezina_vanek}, a modification of this algorithm
+has been actually considered,
+in which each aggregate $N_r$ is made of vertices of $W$ that are \emph{strongly coupled}
+to a certain root vertex $r \in W$, i.e.\
+\[  N_r = \left\{s \in W: |a_{rs}| \geq \theta \sqrt{|a_{rr}a_{ss}|} \right\} \]
+for a given $\theta \in [0,1]$.
+Since the previous algorithm has a sequential nature, a \emph{decoupled} version of
+it has been chosen, where each processor $i$ independently applies the algorithm to
+the set of vertices $W_i^0$ assigned to it in the initial data distribution. This
+version is embarrassingly parallel, since it does not require any data communication.
+On the other hand, it may produce non-uniform aggregates near boundary vertices,
+i.e.\ near vertices adjacent to vertices in other processors, and is strongly
+dependent on the number of processors and on the initial partitioning of the matrix $A$.
+Nevertheless, this algorithm has been chosen for the implementation in MLD2P4,
+since it has been shown to produce good results in practice \cite{Tuminaro_Tong_00}.
+
+The prolongator $P_C=R_C^T$ is built starting from a \emph{tentative prolongator}
+$P \in \Re^{n \times n_C}$, defined as
+\begin{equation} 
+P=(p_{ij}), \quad  p_{ij}= 
+\left\{ \begin{array}{ll}
+1 & \quad \mbox{if} \; i \in V^j_C \\
+0 & \quad \mbox{otherwise}
+\end{array} \right. .
+\label{eq:tent_prol}
+\end{equation}
+$P_C$ is obtained by
+applying to $P$ a smoother $S \in \Re^{n \times n}$:
+\begin{equation}
+P_C = S P,
+\label{eq:smoothed_prol}
+\end{equation}
+in order to remove oscillatory components from the range of the prolongator
+and hence to improve the convergence properties of the multi-level
+Schwarz method \cite{Brezina_Vanek_,StubenGMD69_99}.
+A simple choice for $S$ is the damped Jacobi smoother:
+\begin{equation}
+S = I - \omega D^{-1} A , 
+\label{eq:jac_smoother}
+\end{equation}
+where the value of $\omega$ can be chosen
+using some estimate of the spectral radius of $D^{-1}A$ \cite{Brezina_Vanek}.
+\textbf{Cenno al filtering di $A$ nello smoothing, dicendo che pero' non e' stato
+implementato?}
+
+%%% Local Variables: 
+%%% mode: latex
+%%% TeX-master: "userguide"
+%%% End: 
diff --git a/docs/pdf/bibliography.tex b/docs/pdf/bibliography.tex
index 16a778c7..ecc6e8ee 100644
--- a/docs/pdf/bibliography.tex
+++ b/docs/pdf/bibliography.tex
@@ -1,152 +1,152 @@
-\begin{thebibliography}{99}
-
-%
-\bibitem{PARA04FOREST}
-Bella, G., Filippone, S., De Maio, A., Testa, M.:
-A Simulation Model for Forest Fires.
-In: Dongarra, J., Madsen, K., Wasniewski, J. (eds.):
-Proceedings of PARA~04 Workshop on State of the Art
-in Scientific Computing. Lecture Notes in Computer Science, 3732. Berlin:
-Springer, 2005
-%
-\bibitem{aaecc_07} A. Buttari, D. di Serafino, P. D'Ambra, S. Filippone,\newblock
-2LEV-D2P4: a package of high-performance preconditioners,\newblock
-Applicable Algebra in Engineering, Communications and Computing, 
-Volume 18, Number 3, May, 2007, pp.  223-239
-%Published online: 13 February 2007, {\tt http://dx.doi.org/10.1007/s00200-007-0035-z}
-%
-\bibitem{apnum_07}  P. D'Ambra, S. Filippone,  D. Di Serafino\newblock
-On the Development of PSBLAS-based Parallel Two-level Schwarz Preconditioners
-\newblock
-Applied Numerical Mathematics, Elsevier Science, 
-Volume 57, Issues 11-12, November-December 2007, Pages 1181-1196.
-%published online 3 February 2007, {\tt
-%  http://dx.doi.org/10.1016/j.apnum.2007.01.006}
-
-%% \bibitem{DOUGLAS}
-%% R.E.~Bank and C.C.~Douglas,
-%% {\em SMMP: Sparse Matrix Multiplication Package}, 
-%% Advances in Computational Mathematics, 1993, 1, 127-137.
-%% (See also {\tt http://www.mgnet.org/~douglas/ccd-codes.html}) 
-%
-%
-\bibitem{para_04}
-A.~Buttari, P.~D'Ambra, D.~di Serafino and S.~Filippone,
-{\em Extending PSBLAS to Build Parallel Schwarz Preconditioners},
-in , J.~Dongarra, K.~Madsen, J.~Wasniewski, editors,
-Proceedings of PARA~04 Workshop on State of the Art
-in Scientific Computing, pp.~593--602, Lecture Notes in Computer Science,
-Springer, 2005.
-%
-%% \bibitem{CAI_SAAD}
-%% X.~C.~Cai and Y.~Saad,
-%% {\em Overlapping Domain Decomposition Algorithms for General Sparse Matrices},
-%% Numerical Linear Algebra with Applications, 3(3), pp.~221--237, 1996.
-%% %
-%% \bibitem{CAI_SARKIS}
-%% X.C.~Cai and M.~Sarkis,
-%% {\em A Restricted Additive Schwarz Preconditioner for General Sparse Linear Systems},
-%% SIAM Journal on Scientific Computing, 21(2), pp.~792--797, 1999.
-%
-\bibitem{Cai_Widlund_92}
-X.C.~Cai and O.~B.~Widlund,
-{\em Domain Decomposition Algorithms for Indefinite Elliptic Problems},
-SIAM Journal on Scientific and Statistical Computing, 13(1), pp.~243--258, 1992.
-%
-\bibitem{dd1_94}
-T.~Chan and T.~Mathew,
-{\em Domain Decomposition Algorithms},
-in A.~Iserles, editor, Acta Numerica 1994, pp.~61--143, 1994.
-Cambridge University Press.
-%% %
-%% \bibitem{UMFPACK}
-%% T.A.~Davis, 
-%% {\em Algorithm 832: UMFPACK - an Unsymmetric-pattern Multifrontal
-%% Method with a Column Pre-ordering Strategy},
-%% ACM Transactions on Mathematical Software, 30, pp.~196--199, 2004.
-%% (See also {\tt http://www.cise.ufl.edu/~davis/})
-%% %
-%% \bibitem{SUPERLU}
-%% J.W.~Demmel, S.C.~Eisenstat, J.R.~Gilbert, X.S.~Li and J.W.H.~Liu,
-%% A supernodal approach to sparse partial pivoting,
-%% SIAM Journal on Matrix Analysis and Applications, 20(3), pp.~720--755, 1999.
-%
-\bibitem{BLACS}
-J.~J.~Dongarra and R.~C.~Whaley,
-{\em A User's Guide to the BLACS v.~1.1},
-Lapack Working Note 94, Tech.\ Rep.\ UT-CS-95-281, University of
-Tennessee, March 1995 (updated May 1997).
-%
-\bibitem{sblas_97}
-I.~Duff, M.~Marrone, G.~Radicati and C.~Vittoli,
-{\em Level 3 Basic Linear Algebra Subprograms for Sparse Matrices: 
-a User Level Interface},
-ACM Transactions on Mathematical Software, 23(3), pp.~379--401, 1997.
-%
-\bibitem{sblas_02}
-I.~Duff, M.~Heroux and R.~Pozo,
-{\em An Overview of the Sparse Basic Linear
-Algebra Subprograms: the New Standard from the BLAS Technical Forum},
-ACM Transactions on Mathematical Software, 28(2), pp.~239--267, 2002.
-%
-\bibitem{psblas_00}
-S.~Filippone and M.~Colajanni, 
-{\em PSBLAS: A Library for Parallel Linear Algebra
-Computation on Sparse Matrices},
-\newblock
-ACM Transactions on Mathematical Software, 26(4), pp.~527--550, 2000.
-%
-\bibitem{KIVA3PSBLAS}
-S.~Filippone, P.~D'Ambra, M.~Colajanni,
-{\em Using a Parallel Library of Sparse Linear Algebra in a Fluid Dynamics 
-Applications Code on Linux Clusters},
-in G.~Joubert, A.~Murli, F.~Peters, M.~Vanneschi, editors,
-Parallel Computing - Advances \& Current Issues,
-pp.~441--448, Imperial College Press, 2002. 
-%
-\bibitem{METIS}
-Karypis, G. and Kumar, V.,
-{\em {METIS}: Unstructured Graph Partitioning and Sparse Matrix
-  Ordering System}.
-Minneapolis, MN 55455: University of Minnesota, Department of
-  Computer Science, 1995. 
-Internet Address: {\verb|http://www.cs.umn.edu/~karypis|}.
-\bibitem{BLAS1}
-Lawson, C.,  Hanson, R., Kincaid, D. and Krogh, F.,
-   Basic {L}inear {A}lgebra {S}ubprograms for {F}ortran usage,
-{ACM Trans. Math. Softw.} vol.~{5}, 38--329, 1979.
-
-\bibitem{machiels}
-{Machiels, L. and Deville, M.}
-{\em Fortran 90: An entry to object-oriented programming for the solution
-  of partial differential equations.}
-{ACM Trans. Math. Softw.} vol.~{23}, 32--49.
-\bibitem{metcalf}
-{Metcalf, M., Reid, J. and Cohen, M.}
-{\em Fortran 95/2003 explained.}
-{Oxford University Press}, 2004.
-
-\bibitem{dd2_96}
-B.~Smith, P.~Bjorstad and W.~Gropp,
-{\em Domain Decomposition: Parallel Multilevel Methods for Elliptic
-Partial Differential Equations},
-Cambridge University Press, 1996.
-
-\bibitem{MPI1}
-M.~Snir, S.~Otto, S.~Huss-Lederman, D.~Walker and J.~Dongarra,
-{\em MPI: The Complete Reference. Volume 1 - The MPI Core}, second edition,
-MIT Press, 1998.
-%
-\bibitem{BREZINA_VANEK}
-M.~Brezina and P.~Van{\v e}k,
-{\em A Black-Box Iterative Solver Based on a Two-Level Schwarz Method},
-Computing, 1999, 63, 233-263.
-%
-%
-\bibitem{VANEK_MANDEL_BREZINA}
-P.~Van{\v e}k, J.~Mandel and M.~Brezina,
-{\em Algebraic Multigrid by Smoothed Aggregation for Second and Fourth Order Elliptic Problems},
-Computing, 1996, 56, 179-196.
-%
-
+\begin{thebibliography}{99}
+
+%
+\bibitem{PARA04FOREST}
+Bella, G., Filippone, S., De Maio, A., Testa, M.:
+A Simulation Model for Forest Fires.
+In: Dongarra, J., Madsen, K., Wasniewski, J. (eds.):
+Proceedings of PARA~04 Workshop on State of the Art
+in Scientific Computing. Lecture Notes in Computer Science, 3732. Berlin:
+Springer, 2005
+%
+\bibitem{aaecc_07} A. Buttari, D. di Serafino, P. D'Ambra, S. Filippone,\newblock
+2LEV-D2P4: a package of high-performance preconditioners,\newblock
+Applicable Algebra in Engineering, Communications and Computing, 
+Volume 18, Number 3, May, 2007, pp.  223-239
+%Published online: 13 February 2007, {\tt http://dx.doi.org/10.1007/s00200-007-0035-z}
+%
+\bibitem{apnum_07}  P. D'Ambra, S. Filippone,  D. Di Serafino\newblock
+On the Development of PSBLAS-based Parallel Two-level Schwarz Preconditioners
+\newblock
+Applied Numerical Mathematics, Elsevier Science, 
+Volume 57, Issues 11-12, November-December 2007, Pages 1181-1196.
+%published online 3 February 2007, {\tt
+%  http://dx.doi.org/10.1016/j.apnum.2007.01.006}
+
+%% \bibitem{DOUGLAS}
+%% R.E.~Bank and C.C.~Douglas,
+%% {\em SMMP: Sparse Matrix Multiplication Package}, 
+%% Advances in Computational Mathematics, 1993, 1, 127-137.
+%% (See also {\tt http://www.mgnet.org/~douglas/ccd-codes.html}) 
+%
+%
+\bibitem{para_04}
+A.~Buttari, P.~D'Ambra, D.~di Serafino and S.~Filippone,
+{\em Extending PSBLAS to Build Parallel Schwarz Preconditioners},
+in , J.~Dongarra, K.~Madsen, J.~Wasniewski, editors,
+Proceedings of PARA~04 Workshop on State of the Art
+in Scientific Computing, pp.~593--602, Lecture Notes in Computer Science,
+Springer, 2005.
+%
+%% \bibitem{CAI_SAAD}
+%% X.~C.~Cai and Y.~Saad,
+%% {\em Overlapping Domain Decomposition Algorithms for General Sparse Matrices},
+%% Numerical Linear Algebra with Applications, 3(3), pp.~221--237, 1996.
+%% %
+%% \bibitem{CAI_SARKIS}
+%% X.C.~Cai and M.~Sarkis,
+%% {\em A Restricted Additive Schwarz Preconditioner for General Sparse Linear Systems},
+%% SIAM Journal on Scientific Computing, 21(2), pp.~792--797, 1999.
+%
+\bibitem{Cai_Widlund_92}
+X.C.~Cai and O.~B.~Widlund,
+{\em Domain Decomposition Algorithms for Indefinite Elliptic Problems},
+SIAM Journal on Scientific and Statistical Computing, 13(1), pp.~243--258, 1992.
+%
+\bibitem{dd1_94}
+T.~Chan and T.~Mathew,
+{\em Domain Decomposition Algorithms},
+in A.~Iserles, editor, Acta Numerica 1994, pp.~61--143, 1994.
+Cambridge University Press.
+%% %
+%% \bibitem{UMFPACK}
+%% T.A.~Davis, 
+%% {\em Algorithm 832: UMFPACK - an Unsymmetric-pattern Multifrontal
+%% Method with a Column Pre-ordering Strategy},
+%% ACM Transactions on Mathematical Software, 30, pp.~196--199, 2004.
+%% (See also {\tt http://www.cise.ufl.edu/~davis/})
+%% %
+%% \bibitem{SUPERLU}
+%% J.W.~Demmel, S.C.~Eisenstat, J.R.~Gilbert, X.S.~Li and J.W.H.~Liu,
+%% A supernodal approach to sparse partial pivoting,
+%% SIAM Journal on Matrix Analysis and Applications, 20(3), pp.~720--755, 1999.
+%
+\bibitem{BLACS}
+J.~J.~Dongarra and R.~C.~Whaley,
+{\em A User's Guide to the BLACS v.~1.1},
+Lapack Working Note 94, Tech.\ Rep.\ UT-CS-95-281, University of
+Tennessee, March 1995 (updated May 1997).
+%
+\bibitem{sblas_97}
+I.~Duff, M.~Marrone, G.~Radicati and C.~Vittoli,
+{\em Level 3 Basic Linear Algebra Subprograms for Sparse Matrices: 
+a User Level Interface},
+ACM Transactions on Mathematical Software, 23(3), pp.~379--401, 1997.
+%
+\bibitem{sblas_02}
+I.~Duff, M.~Heroux and R.~Pozo,
+{\em An Overview of the Sparse Basic Linear
+Algebra Subprograms: the New Standard from the BLAS Technical Forum},
+ACM Transactions on Mathematical Software, 28(2), pp.~239--267, 2002.
+%
+\bibitem{psblas_00}
+S.~Filippone and M.~Colajanni, 
+{\em PSBLAS: A Library for Parallel Linear Algebra
+Computation on Sparse Matrices},
+\newblock
+ACM Transactions on Mathematical Software, 26(4), pp.~527--550, 2000.
+%
+\bibitem{KIVA3PSBLAS}
+S.~Filippone, P.~D'Ambra, M.~Colajanni,
+{\em Using a Parallel Library of Sparse Linear Algebra in a Fluid Dynamics 
+Applications Code on Linux Clusters},
+in G.~Joubert, A.~Murli, F.~Peters, M.~Vanneschi, editors,
+Parallel Computing - Advances \& Current Issues,
+pp.~441--448, Imperial College Press, 2002. 
+%
+\bibitem{METIS}
+Karypis, G. and Kumar, V.,
+{\em {METIS}: Unstructured Graph Partitioning and Sparse Matrix
+  Ordering System}.
+Minneapolis, MN 55455: University of Minnesota, Department of
+  Computer Science, 1995. 
+Internet Address: {\verb|http://www.cs.umn.edu/~karypis|}.
+\bibitem{BLAS1}
+Lawson, C.,  Hanson, R., Kincaid, D. and Krogh, F.,
+   Basic {L}inear {A}lgebra {S}ubprograms for {F}ortran usage,
+{ACM Trans. Math. Softw.} vol.~{5}, 38--329, 1979.
+
+\bibitem{machiels}
+{Machiels, L. and Deville, M.}
+{\em Fortran 90: An entry to object-oriented programming for the solution
+  of partial differential equations.}
+{ACM Trans. Math. Softw.} vol.~{23}, 32--49.
+\bibitem{metcalf}
+{Metcalf, M., Reid, J. and Cohen, M.}
+{\em Fortran 95/2003 explained.}
+{Oxford University Press}, 2004.
+
+\bibitem{dd2_96}
+B.~Smith, P.~Bjorstad and W.~Gropp,
+{\em Domain Decomposition: Parallel Multilevel Methods for Elliptic
+Partial Differential Equations},
+Cambridge University Press, 1996.
+
+\bibitem{MPI1}
+M.~Snir, S.~Otto, S.~Huss-Lederman, D.~Walker and J.~Dongarra,
+{\em MPI: The Complete Reference. Volume 1 - The MPI Core}, second edition,
+MIT Press, 1998.
+%
+\bibitem{BREZINA_VANEK}
+M.~Brezina and P.~Van{\v e}k,
+{\em A Black-Box Iterative Solver Based on a Two-Level Schwarz Method},
+Computing, 1999, 63, 233-263.
+%
+%
+\bibitem{VANEK_MANDEL_BREZINA}
+P.~Van{\v e}k, J.~Mandel and M.~Brezina,
+{\em Algebraic Multigrid by Smoothed Aggregation for Second and Fourth Order Elliptic Problems},
+Computing, 1996, 56, 179-196.
+%
+
 \end{thebibliography}
\ No newline at end of file
diff --git a/docs/pdf/building.tex b/docs/pdf/building.tex
index e6acbbf4..686b3522 100644
--- a/docs/pdf/building.tex
+++ b/docs/pdf/building.tex
@@ -1,7 +1,7 @@
-\section{Configuring and Building MLD2P4\label{sec:configuring}}
-    - uso di GNU autoconf e automake \\
-    - software di base necessario (MPI, BLACS, BLAS, PSBLAS - specificare versioni) \\
-    - software opzionale (UMFPACK, SuperLU, SuperLUdist - specificare versioni e opzioni di configure) \\
-    - sistemi operativi e compilatori su cui MLD2P4 e' stato costruito con successo \\
-    - sono previste opzioni di configurazione per il debugging o per il profiling? \\
-    - albero delle directory \\
+\section{Configuring and Building MLD2P4\label{sec:configuring}}
+    - uso di GNU autoconf e automake \\
+    - software di base necessario (MPI, BLACS, BLAS, PSBLAS - specificare versioni) \\
+    - software opzionale (UMFPACK, SuperLU, SuperLUdist - specificare versioni e opzioni di configure) \\
+    - sistemi operativi e compilatori su cui MLD2P4 e' stato costruito con successo \\
+    - sono previste opzioni di configurazione per il debugging o per il profiling? \\
+    - albero delle directory \\
diff --git a/docs/pdf/conventions.tex b/docs/pdf/conventions.tex
index 39c91f22..7540020d 100644
--- a/docs/pdf/conventions.tex
+++ b/docs/pdf/conventions.tex
@@ -1,6 +1,6 @@
-\section{Notational Conventions\label{sec:conventions}}
-    - caratteri tipografici usati nella guida (vedi guida ML recente e guida Aztec) \\
-    - convenzioni sui nomi di routine (differenza tra high-level e medium-level),
-      strutture dati,\\
-      moduli, costanti, etc. (vedi guida psblas) \\
+\section{Notational Conventions\label{sec:conventions}}
+    - caratteri tipografici usati nella guida (vedi guida ML recente e guida Aztec) \\
+    - convenzioni sui nomi di routine (differenza tra high-level e medium-level),
+      strutture dati,\\
+      moduli, costanti, etc. (vedi guida psblas) \\
     - versione reale e complessa\\
\ No newline at end of file
diff --git a/docs/pdf/distribution.tex b/docs/pdf/distribution.tex
index 3d8f75e9..75a22a02 100644
--- a/docs/pdf/distribution.tex
+++ b/docs/pdf/distribution.tex
@@ -1,41 +1,42 @@
-\section{Code Distribution\label{sec:distribution}}
-
-The MLD2P4 is freely distributable under the following copyright
-terms:
-\begin{verbatim} 
-                         MLD2P4  version 1.0
-MultiLevel Domain Decomposition Parallel Preconditioners Package
-           based on PSBLAS (Parallel Sparse BLAS version 2.3)
-
-(C) Copyright 2008
-
-                    Salvatore Filippone  University of Rome Tor Vergata       
-                    Alfredo Buttari      University of Rome Tor Vergata
-                    Pasqua D'Ambra       ICAR-CNR, Naples
-                    Daniela di Serafino  Second University of Naples
-
-
-Redistribution and use in source and binary forms, with or without
-modification, are permitted provided that the following conditions
-are met:
-  1. Redistributions of source code must retain the above copyright
-     notice, this list of conditions and the following disclaimer.
-  2. Redistributions in binary form must reproduce the above copyright
-     notice, this list of conditions, and the following disclaimer in the
-     documentation and/or other materials provided with the distribution.
-  3. The name of the MLD2P4 group or the names of its contributors may
-     not be used to endorse or promote products derived from this
-     software without specific written permission.
-
-THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
-``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
-TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
-PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE MLD2P4 GROUP OR ITS CONTRIBUTORS
-BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
-CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
-SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
-INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
-CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
-ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
-POSSIBILITY OF SUCH DAMAGE.
-\end{verbatim}
+\section{Code Distribution\label{sec:distribution}}
+
+The MLD2P4 is freely distributable under the following copyright
+terms: {\small
+\begin{verbatim} 
+                         MLD2P4  version 1.0
+MultiLevel Domain Decomposition Parallel Preconditioners Package
+           based on PSBLAS (Parallel Sparse BLAS version 2.3)
+
+(C) Copyright 2008
+
+                    Salvatore Filippone  University of Rome Tor Vergata       
+                    Alfredo Buttari      University of Rome Tor Vergata
+                    Pasqua D'Ambra       ICAR-CNR, Naples
+                    Daniela di Serafino  Second University of Naples
+
+
+Redistribution and use in source and binary forms, with or without
+modification, are permitted provided that the following conditions
+are met:
+  1. Redistributions of source code must retain the above copyright
+     notice, this list of conditions and the following disclaimer.
+  2. Redistributions in binary form must reproduce the above copyright
+     notice, this list of conditions, and the following disclaimer in the
+     documentation and/or other materials provided with the distribution.
+  3. The name of the MLD2P4 group or the names of its contributors may
+     not be used to endorse or promote products derived from this
+     software without specific written permission.
+
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
+TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
+PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE MLD2P4 GROUP OR ITS CONTRIBUTORS
+BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
+CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
+SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
+INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
+CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
+ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+POSSIBILITY OF SUCH DAMAGE.
+\end{verbatim}
+}
\ No newline at end of file
diff --git a/docs/pdf/errors.tex b/docs/pdf/errors.tex
index 2ba4f60b..5952557d 100644
--- a/docs/pdf/errors.tex
+++ b/docs/pdf/errors.tex
@@ -1,9 +1,9 @@
-\section{Error Handling}\label{sec:errors}
-
-Error handling
-    - Breve descrizione con rinvio alla guida di PSBLAS
-
-%%% Local Variables: 
-%%% mode: latex
-%%% TeX-master: "userguide"
-%%% End: 
+\section{Error Handling}\label{sec:errors}
+
+Error handling
+    - Breve descrizione con rinvio alla guida di PSBLAS
+
+%%% Local Variables: 
+%%% mode: latex
+%%% TeX-master: "userguide"
+%%% End: 
diff --git a/docs/pdf/gettingstarted.tex b/docs/pdf/gettingstarted.tex
index 92c81021..21071d11 100644
--- a/docs/pdf/gettingstarted.tex
+++ b/docs/pdf/gettingstarted.tex
@@ -1,224 +1,231 @@
-\section{Getting Started\label{sec:started}}
-
-We describe the basics for building and applying MLD2P4 one-level and multi-level
-Schwarz preconditioners with the Krylov solvers included in PSBLAS \cite{}.
-The following five steps are required:
-\begin{enumerate}
-\item \emph{Allocate and initialize the preconditioner data structure, according to
-	a preconditioner type chosen by the user}. This is performed by the routine
-	\verb|mld_precinit|, which also sets a default preconditioner for each preconditioner
-	type selected by the user. The default preconditioner associated to each preconditioner
-	type is listed in Table~\ref{tab:precinit}; the string used by \verb|mld_precinit|
-	to identify each preconditioner type is also given. The preconditioner data structure is
-	the derived data type \verb|mld_prec_type|, which is accessed to the user only
-	through the MLD2P4 routines.
-\item \emph{Choose a specific variant of the selected preconditioner type, by setting
-  the preconditioner parameters.} This is performed by the routine \verb|mld_precset|.
-  A few examples concerning the use of \verb|mld_precset| are given in 
-  Sections~\ref{sec:example1} and \ref{sec:example1}; a complete list of all the
-  preconditioner parameters and their allowed values is provided in 
-  Section~\ref{sec:highlevel}. 
-\item \emph{Build the preconditioner for a given matrix.} This is performed by
-  the routine \verb|mld_precbld|.
-\item \emph{Apply the preconditioner at each iteration of a Krylov solver.}
-  This is performed by the routine \verb|mld_precaply|. When using the PSBLAS Krylov solvers,
-  this step is completely transparent to the user, since \verb|mld_precaply| is called
-  by the PSBLAS routine implementing the Krylov solver (\verb|psb_krylov|).
-\item \emph{Deallocate the preconditioner data structure}. This is performed by
-  the routine \verb|mld_precfree|. This step is complementary to step 1 and should
-  be performed when the preconditioner is no more used.
-\end{enumerate}
-A detailed description of the above routines is given in Section~\ref{sec:highlevel}.
-
-Note that the Fortran 95 module \verb|mld_prec_mod| must be used in the program
-calling the MLD2P4 routines. Furthermore, to apply MLD2P4 with the Krylov solvers
-from PSBLAS, the module \verb|psb_krylov_mod| must be used too.
-
-Two simple example programs showing the (basic) use of MLD2P4 are reported in
-Section~\ref{sec:examples}.
-
-\begin{table}[th]
-{
-\begin{center}
-\begin{tabular}{|l|l|p{6.7cm}|}
-\hline
-Type              & String & Default preconditioner \\ \hline
-No preconditioner &'NOPREC'& (Considered only to use the PSBLAS
-                             Krylov solvers with no preconditioner.) \\
-Diagonal          & 'DIAG' & --- \\
-Block Jacobi      & 'BJAC' & ILU(0) on the local blocks.\\ 
-Additive Schwarz  & 'AS'   & Restricted Additive Schwarz (RAS),
-                             with overlap 1 and ILU(0) on the local blocks. \\ 
-Multilevel        &'ML'    & Multi-level hybrid preconditioner (additive on the
-                             same level and multiplicative through the levels),
-                             with post-smoothing only. Number of levels: 2;
-                             post-smoother: block-Jacobi preconditioner, with ILU(0)
-                             on the local blocks; coarsest matrix: distributed among the
-                             processors; corase-level solver: 4 sweeps of the
-                             block-Jacobi solver, with ILU(0) on the blocks. \\
-\hline
-\end{tabular}
-\end{center}
-}
-\caption{Preconditioner types and default choices.\label{tab:precinit}}
-\end{table}
-
-\subsection{Examples\label{sec:examples}}
-
-The simple code reported below shows how to set and apply the MLD2P4 default multi-level
-preconditioned, i.e.\ the two-level hybrid post-smoothed Schwarz preconditioner, using block-Jacobi with ILU(0) on the blocks as basic preconditioner,
-a coarse matrix distributed among the processors, and four block-Jacobi sweeps with ILU(0) on the blocks as approximate coarse-level solver. The choice of this preconditioner is made
-by simply specifying \verb|'ML'| as second argument of \verb|mld_precinit|
-(a call to \verb|mld_precset| is not needed).
-The preconditioner is applied within the BiCGSTAB solver provided by PSBLAS. 
-
-The part of the code concerning the
-reading and assembling of the sparse matrix and the right-hand side vector, performed
-through the PSBLAS routines for sparse matrix and vector management, is not reported
-here for brevity. Other statements concerning the use of PSBLAS are neglected too.
-The complete code can be found in the example program file \verb|example_2lev_default.f90|
-in the directory \textbf{XXXXXX (SPECIFICARE).} Note that the modules \verb|psb_base_mod|
-and \verb|psb_util_mod| at the beginning of the code are required by PSBLAS.
-For details on the use of the PSBLAS routines, see the PSBLAS User's Guide \cite{}.
-
-\begin{verbatim}
-  use psb_base_mod
-  use psb_util_mod 
-  use mld_prec_mod
-  use psb_krylov_mod
-... ...
-!
-! sparse matrix
-  type(psb_dspmat_type) :: A
-! sparse matrix descriptor
-  type(psb_desc_type)   :: DESC_A
-! preconditioner
-  type(mld_prec_type)  :: PRE
-... ...
-!
-! initialize the parallel environment
-  call psb_init(ictxt)
-  call psb_info(ictxt,iam,np)
-... ...
-!
-! read and assemble the matrix A and the right-hand
-! side b using PSBLAS routines for sparse matrix /
-! vector management
-... ...
-!
-! initialize the default multi-level preconditioner
-! (two-level hybrid post-smoothed Schwarz)
-  call mld_precinit(PRE,'ML',info)
-!
-! build the preconditioner
-  call psb_precbld(A,PRE,DESC_A,info)
-!
-! set the solver parameters and the initial guess
-  ... ...
-!
-! solve Ax=b with preconditioned BiCGSTAB
-  call psb_krylov('BICGSTAB',A,PRE,b,x,tol,DESC_A,info)
-  ... ...
-!
-! cleanup the preconditioner
-  call mld_precfree(PRE,info)
-!
-! cleanup other data structures
-  ... ...
-!
-! exit the parallel environment
-  call psb_exit(ictxt)
-  stop
-\end{verbatim}
-
-
-\textbf{MODIFICARE TUTTA LA PARTE CHE SEGUE:\\
-- solo istruzioni diverse dall'esempio precedente (essenzialmente il setting del precondizionatore, magari con piu' chiamate a precset;\\
-- lasciare l'osservazione sulla specifica esplicita del numero di livelli;\\
-- rimandare al paragrafo successivo per una decrizione accurata di tutti i parametri;\\
-- lasciare l'osservazione sui vecchi utenti di PSBLAS.}\\
-
-In the following we describe the general procedure for setting and building one of the MLD2P4 preconditioners.
-The user has first to prepare the preconditioner data structure by using the routine \verb|mld_precinit|. Input parameters
-for this routine include a string parameter, needed to define the preconditioner type, and an optional integer parameter
-specifying the number of the levels in the case of a multi-level preconditioner.
-Note that if the optional parameter is not present and a multi-level preconditioner has been chosen,
-a two-level preconditioner is set. On the other hand, the integer parameter is ignored if the type of the preconditioner is not multilevel.
-In Table \ref{tab:precinit} we report both the possible choices for the preconditioner type
-and the related default preconditioners. 
-
-
-The user of MLD2P4 may set a lot of parameters for one-level and multi-level Schwarz, in order
-to define a different preconditioner than that of default choices. The parameters
-can be set through the routine \verb|mld_precset|. The APIs of \verb|mld_precinit| and  \verb|mld_precset| as well as the complete 
-list of the parameters that can be set with the corresponding allowed values are reported in Section \ref{sec:highlevel}. In the following a simple code
-for a three-level hybrid post-smoothed Schwarz preconditioner, using RAS with overlap 1 as local preconditioner,
-with ILU(0) on the local blocks, a distributed coarse matrix, four block-Jacobi sweeps with the UMFPACK LU
-factorization on the blocks as coarse-matrix solver, is reported. Note that for the multi-level preconditioners, the levels are numbered in increasing
-order starting from the finest one, i.e. level 1 is the finest level. 
-For more details, see the test program \verb|example2.f90| in xxxx(directory dei test).\\[0.5cm]
-
-\begin{verbatim}
-  use psb_base_mod
-  use psb_util_mod 
-  use mld_prec_mod
-  use psb_krylov_mod
-... ...
-!
-! sparse matrix
-  type(psb_dspmat_type) :: A
-! sparse matrix descriptor
-  type(psb_desc_type)   :: DESC_A
-! preconditioner data
-  type(mld_dprec_type)  :: PRE
-... ...
-!
-! initialization of the parallel environment
-
-  call psb_init(ictxt)
-  call psb_info(ictxt,iam,np)
-... ...
-! read and assemble the matrix A and the right-hand
-! side vector b using PSBLAS routines for sparse
-! matrix/vector management
-... ...
-! prepare the three-level hybrid post-smoothed Schwarz
-! using RAS with overlap 1 as local preconditioner
-!
-  call mld_precinit(PRE,'ML',info,nlev=3)
-  call mld_precset(PRE,mld_n_ovr_,novr=1,info,ilev=1)
-  call mld_precset(PRE,mld_sub_restr_,psb_halo_,info,ilev=1)
-NOTA: e' PROPRIO BRUTTO "PSB_HALO_", BISOGNEREBBE AVERE COSTANTI CHE HANNO IL PREFISSO MLD!
-!
-! build preconditioner
-  call psb_precbld(A,PRE,DESC_A,info)
-!
-! set solver parameters and initial guess
-  ... ...
-! solve Ax=b with preconditioned BiCGSTAB
-
-  call psb_krylov('BICGSTAB',A,PRE,b,x,tol,DESC_A,info)
-  ... ...
-!  
-!  cleanup storage and exit
-!
-  call mld_precfree(PRE,info)
-!
-  call psb_gefree(b,DESC_A,info)
-  call psb_gefree(x,DESC_A,info)
-  call psb_spfree(A,DESC_A,info)
-  call psb_cdfree(DESC_A,info)
-!
-  call psb_exit(ictxt)
-  stop
-
-\end{verbatim}
-
-{\bf Remark for users with PSBLAS-based legacy codes:} when MLD2P4 is installed, a PSBLAS user, with a PSBLAS-based legacy code 
-calling base preconditioners included in PSBLAS (NOPREC, DIAG and BJAC), is able to use the same preconditioners without changes to the code, if she/he
-includes in her/his program the file \verb|psb_prec_mod|.
-
-%%% Local Variables: 
-%%% mode: latex
-%%% TeX-master: "userguide"
-%%% End: 
+\section{Getting Started\label{sec:started}}
+
+We describe the basics for building and applying MLD2P4 one-level and multi-level
+Schwarz preconditioners with the Krylov solvers included in PSBLAS \cite{}.
+The following steps are required:
+\begin{enumerate} 
+\item \emph{Declare the preconditioner data structure}. It is a derived data type,
+  \verb|mld_|\emph{x}\verb|prec_type|,where \emph{x} may be \verb|s|, \verb|d|, \verb|c|
+	or \verb|z|, according to the basic data type of the sparse matrix
+	(\verb|s| = real single precision; \verb|s| = real double precision;
+	\verb|c| = complex single precision; \verb|z| = complex double precision).
+	This data structure is accessed by the user only through the MLD2P4 routines,
+	following an object-oriented approach.
+\item \emph{Allocate and initialize the preconditioner data structure, according to
+	a preconditioner type chosen by the user}. This is performed by the routine
+	\verb|mld_precinit|, which also sets a default preconditioner for each preconditioner
+	type selected by the user. The default preconditioner associated to each preconditioner
+	type is listed in Table~\ref{tab:precinit}; the string used by \verb|mld_precinit|
+	to identify each preconditioner type is also given.
+\item \emph{Choose a specific preconditioner within the selected preconditioner type, by setting
+  the preconditioner parameters.} This is performed by the routine \verb|mld_precset|.
+  A few examples concerning the use of \verb|mld_precset| are given in 
+  Section~\ref{sec:examples}; a complete list of all the
+  preconditioner parameters and their allowed values is provided in 
+  Section~\ref{sec:highlevel}. 
+\item \emph{Build the preconditioner for a given matrix.} This is performed by
+  the routine \verb|mld_precbld|.
+\item \emph{Apply the preconditioner at each iteration of a Krylov solver.}
+  This is performed by the routine \verb|mld_precaply|. When using the PSBLAS Krylov solvers,
+  this step is completely transparent to the user, since \verb|mld_precaply| is called
+  by the PSBLAS routine implementing the Krylov solver (\verb|psb_krylov|).
+\item \emph{Deallocate the preconditioner data structure}. This is performed by
+  the routine \verb|mld_precfree|. This step is complementary to step 1 and should
+  be performed when the preconditioner is no more used.
+\end{enumerate}
+A detailed description of the above routines is given in Section~\ref{sec:highlevel}.
+
+Note that the Fortran 95 module \verb|mld_prec_mod| must be used in the program
+calling the MLD2P4 routines. Furthermore, to apply MLD2P4 with the Krylov solvers
+from PSBLAS, the module \verb|psb_krylov_mod| must be used too.
+
+Examples showing the basic use of MLD2P4 are reported in Section~\ref{sec:examples}.
+
+\begin{table}[th]
+{
+\begin{center}
+\begin{tabular}{|l|l|p{6.7cm}|}
+\hline
+Type              & String        & Default preconditioner \\ \hline
+No preconditioner &\verb|'NOPREC'|& (Considered only to use the PSBLAS
+                                    Krylov solvers with no preconditioner.) \\
+Diagonal          & \verb|'DIAG'| & --- \\
+Block Jacobi      & \verb|'BJAC'| & Block Jacobi with ILU(0) on the local blocks.\\ 
+Additive Schwarz  & \verb|'AS'|   & Restricted Additive Schwarz (RAS),
+                                    with overlap 1 and ILU(0) on the local blocks. \\ 
+Multilevel        &\verb|'ML'|    & Multi-level hybrid preconditioner (additive on the
+                                    same level and multiplicative through the levels),
+                                    with post-smoothing only. Number of levels: 2;
+                                    post-smoother: block-Jacobi preconditioner with ILU(0)
+                                    on the local blocks; coarsest matrix: distributed among the
+                                    processors; corase-level solver: 4 sweeps of the
+                                    block-Jacobi solver, with ILU(0) on the blocks. \\
+\hline
+\end{tabular}
+\end{center}
+}
+\caption{Preconditioner types and default choices.\label{tab:precinit}}
+\end{table}
+
+\subsection{Examples\label{sec:examples}}
+
+The code reported below shows how to set and apply the MLD2P4 default multi-level
+preconditioned, i.e.\ the two-level hybrid post-smoothed Schwarz preconditioner,
+using block-Jacobi with ILU(0) on the blocks as basic preconditioner,
+a coarse matrix distributed among the processors, and four block-Jacobi
+sweeps with ILU(0) on the blocks as approximate coarse-level solver.
+The choice of this preconditioner is made
+by simply specifying \verb|'ML'| as second argument of \verb|mld_precinit|
+(a call to \verb|mld_precset| is not needed).
+The preconditioner is applied within the BiCGSTAB solver provided by PSBLAS. 
+
+The part of the code concerning the
+reading and assembling of the sparse matrix and the right-hand side vector, performed
+through the PSBLAS routines for sparse matrix and vector management, is not reported
+here for brevity. Other statements concerning the use of PSBLAS are neglected too.
+The complete code can be found in the example program file \verb|example_2lev_default.f90|
+in the directory \textbf{XXXXXX (SPECIFICARE).} Note that the modules \verb|psb_base_mod|
+and \verb|psb_util_mod| at the beginning of the code are required by PSBLAS.
+For details on the use of the PSBLAS routines, see the PSBLAS User's Guide \cite{}.
+
+\begin{verbatim}
+  use psb_base_mod
+  use psb_util_mod 
+  use mld_prec_mod
+  use psb_krylov_mod
+... ...
+!
+! sparse matrix
+  type(psb_dspmat_type) :: A
+! sparse matrix descriptor
+  type(psb_desc_type)   :: DESC_A
+! preconditioner
+  type(mld_dprec_type)  :: PRE
+... ...
+!
+! initialize the parallel environment
+  call psb_init(ictxt)
+  call psb_info(ictxt,iam,np)
+... ...
+!
+! read and assemble the matrix A and the right-hand
+! side b using PSBLAS routines for sparse matrix /
+! vector management
+... ...
+!
+! initialize the default multi-level preconditioner
+! (two-level hybrid post-smoothed Schwarz)
+  call mld_precinit(PRE,'ML',info)
+!
+! build the preconditioner
+  call psb_precbld(A,PRE,DESC_A,info)
+!
+! set the solver parameters and the initial guess
+  ... ...
+!
+! solve Ax=b with preconditioned BiCGSTAB
+  call psb_krylov('BICGSTAB',A,PRE,b,x,tol,DESC_A,info)
+  ... ...
+!
+! cleanup the preconditioner
+  call mld_precfree(PRE,info)
+!
+! cleanup other data structures
+  ... ...
+!
+! exit the parallel environment
+  call psb_exit(ictxt)
+  stop
+\end{verbatim}
+
+
+\textbf{MODIFICARE TUTTA LA PARTE CHE SEGUE:\\
+- solo istruzioni diverse dall'esempio precedente (essenzialmente il setting del precondizionatore, magari con piu' chiamate a precset;\\
+- lasciare l'osservazione sulla specifica esplicita del numero di livelli;\\
+- rimandare al paragrafo successivo per una decrizione accurata di tutti i parametri;\\
+- lasciare l'osservazione sui vecchi utenti di PSBLAS.}\\
+
+In the following we describe the general procedure for setting and building one of the MLD2P4 preconditioners.
+The user has first to prepare the preconditioner data structure by using the routine \verb|mld_precinit|. Input parameters
+for this routine include a string parameter, needed to define the preconditioner type, and an optional integer parameter
+specifying the number of the levels in the case of a multi-level preconditioner.
+Note that if the optional parameter is not present and a multi-level preconditioner has been chosen,
+a two-level preconditioner is set. On the other hand, the integer parameter is ignored if the type of the preconditioner is not multilevel.
+In Table \ref{tab:precinit} we report both the possible choices for the preconditioner type
+and the related default preconditioners. 
+
+
+The user of MLD2P4 may set a lot of parameters for one-level and multi-level Schwarz, in order
+to define a different preconditioner than that of default choices. The parameters
+can be set through the routine \verb|mld_precset|. The APIs of \verb|mld_precinit| and  \verb|mld_precset| as well as the complete 
+list of the parameters that can be set with the corresponding allowed values are reported in Section \ref{sec:highlevel}. In the following a simple code
+for a three-level hybrid post-smoothed Schwarz preconditioner, using RAS with overlap 1 as local preconditioner,
+with ILU(0) on the local blocks, a distributed coarse matrix, four block-Jacobi sweeps with the UMFPACK LU
+factorization on the blocks as coarse-matrix solver, is reported. Note that for the multi-level preconditioners, the levels are numbered in increasing
+order starting from the finest one, i.e. level 1 is the finest level. 
+For more details, see the test program \verb|example2.f90| in xxxx(directory dei test).\\[0.5cm]
+
+\begin{verbatim}
+  use psb_base_mod
+  use psb_util_mod 
+  use mld_prec_mod
+  use psb_krylov_mod
+... ...
+!
+! sparse matrix
+  type(psb_dspmat_type) :: A
+! sparse matrix descriptor
+  type(psb_desc_type)   :: DESC_A
+! preconditioner data
+  type(mld_dprec_type)  :: PRE
+... ...
+!
+! initialization of the parallel environment
+
+  call psb_init(ictxt)
+  call psb_info(ictxt,iam,np)
+... ...
+! read and assemble the matrix A and the right-hand
+! side vector b using PSBLAS routines for sparse
+! matrix/vector management
+... ...
+! prepare the three-level hybrid post-smoothed Schwarz
+! using RAS with overlap 1 as local preconditioner
+!
+  call mld_precinit(PRE,'ML',info,nlev=3)
+  call mld_precset(PRE,mld_n_ovr_,novr=1,info,ilev=1)
+  call mld_precset(PRE,mld_sub_restr_,psb_halo_,info,ilev=1)
+NOTA: e' PROPRIO BRUTTO "PSB_HALO_", BISOGNEREBBE AVERE COSTANTI CHE HANNO IL PREFISSO MLD!
+!
+! build preconditioner
+  call psb_precbld(A,PRE,DESC_A,info)
+!
+! set solver parameters and initial guess
+  ... ...
+! solve Ax=b with preconditioned BiCGSTAB
+
+  call psb_krylov('BICGSTAB',A,PRE,b,x,tol,DESC_A,info)
+  ... ...
+!  
+!  cleanup storage and exit
+!
+  call mld_precfree(PRE,info)
+!
+  call psb_gefree(b,DESC_A,info)
+  call psb_gefree(x,DESC_A,info)
+  call psb_spfree(A,DESC_A,info)
+  call psb_cdfree(DESC_A,info)
+!
+  call psb_exit(ictxt)
+  stop
+
+\end{verbatim}
+
+{\bf Remark for users with PSBLAS-based legacy codes:} when MLD2P4 is installed, a PSBLAS user, with a PSBLAS-based legacy code 
+calling base preconditioners included in PSBLAS (NOPREC, DIAG and BJAC), is able to use the same preconditioners without changes to the code, if she/he
+includes in her/his program the file \verb|psb_prec_mod|.
+
+%%% Local Variables: 
+%%% mode: latex
+%%% TeX-master: "userguide"
+%%% End: 
diff --git a/docs/pdf/listofroutines.tex b/docs/pdf/listofroutines.tex
index 0829ef60..3b508699 100644
--- a/docs/pdf/listofroutines.tex
+++ b/docs/pdf/listofroutines.tex
@@ -1,10 +1,10 @@
-\section{List of Routines}\label{sec:routines}
-
-   Elenco (ordine alfabetico) di tutte le routine, con rinvio (ipertestuale e num. pag.) alla descrizione
-     di ciascuna in qualche paragrafo precedente
-     (una specie di indice analitico, che rimanda alle routine descritte precedentemente nei rispettivi paragrafi)
-
-%%% Local Variables: 
-%%% mode: latex
-%%% TeX-master: "userguide"
-%%% End: 
+\section{List of Routines}\label{sec:routines}
+
+   Elenco (ordine alfabetico) di tutte le routine, con rinvio (ipertestuale e num. pag.) alla descrizione
+     di ciascuna in qualche paragrafo precedente
+     (una specie di indice analitico, che rimanda alle routine descritte precedentemente nei rispettivi paragrafi)
+
+%%% Local Variables: 
+%%% mode: latex
+%%% TeX-master: "userguide"
+%%% End: 
diff --git a/docs/pdf/overview.tex b/docs/pdf/overview.tex
index eac4bac9..7278dae3 100644
--- a/docs/pdf/overview.tex
+++ b/docs/pdf/overview.tex
@@ -1,62 +1,62 @@
-\section{General Overview\label{sec:overview}}
-
-The \emph{Multi-Level Domain Decomposition Parallel Preconditioners Package based on
-PSBLAS (MLD2P4}) provides various versions of multi-level Schwarz preconditioners~\cite{DD2},
-to be used in the iterative solutions of sparse linear systems $Ax=b$, where
-$A$ is a square, real or complex, sparse matrix with a symmetric sparsity pattern.
-\textbf{Ma non abbiamo detto che, se il pattern di sparista' non e' simmetrico,
-lavoriamo su $(A+A^T)/2$? Ma questo vale solo per l'aggregazione? Dovremmo fare
-qualcosa di consistente anche con 1-lev Schwarz.}
-Both additive and hybrid preconditioners, i.e.\ multiplicative among the levels
-and additive inside a level, are implemented; the basic additive Schwarz preconditioners
-are obtained by considering only one level. A purely algebraic approach is used to
-generate a sequence of coarse-level corrections to a basic preconditioner, without
-explicitly using any information on the geometry of the original problem (e.g.\ the
-discretization of a PDE). The smoothed aggregation technique is applied
-as algebraic coarsening strategy~\cite{}.
-
-The package is written in Fortran~95, using object-oriented techniques,
-and is based on a distributed-memory parallel programming paradigm. \textbf{SALVATORE,
-potresti aggiungere due righe sulla scelta del Fortran 95 e sul semplice interfacciamento
-con i legacy codes, senza ripetere quello che e' detto sotto sulla scelta di PSBLAS?}
-Single and double precision implementations of MLD2P4 are available for both the
-real and the complex case, that can be used through a single interface.
-\textbf{SALVATORE, funziona tutto?}
-
-MLD2P4 has been designed to implement scalable and easy-to-use multilevel preconditioners
-in the context of the PSBLAS (Parallel Sparse BLAS) computational framework~\cite{}.
-PSBLAS is a library originally developed to address the parallel implementation of
-iterative solvers for sparse linear system, by providing basic linear algebra
-operators and data management facilities for distributed sparse matrices; it
-also includes parallel Krylov solvers, built on the top of the basic PSBLAS kernels.
-The preconditioners available in MLD2P4 can be used with these Krylov solvers.
-The choice of PSBLAS has been mainly motivated by the need of having
-a portable and efficient software infrastructure implementing ``de facto'' standard
-parallel sparse linear algebra kernels, to pursue goals such as performance,
-portability, modularity ed extensibility in the development of the preconditioner
-package. On the other hand, the implementation of MLD2P4 has led to some
-revisions and extentions of the PSBLAS kernels, leading to the
-recent PSBLAS 2.0 version~\cite{}. The inter-process comunication required
-by MLD2P4 is encapsulated into the PSBLAS routines, except few cases where
-MPI~\cite{} is explicitly called. Therefore, MLD2P4 can be run on any parallel
-machine where PSBLAS and MPI implementations are available.
-
-MLD2P4 has a layered and modular software architecture where three main layers can be identified. The lower layer consists of the PSBLAS kernels, the middle one implements
-the construction and application phases of the preconditioners, and the upper one
-provides a uniform and easy-to-use interface to all the preconditioners. 
-This architecture allows for different levels of use of the package:
-few black-box routines at the upper level allow non-expert users to easily
-build any preconditioner available in MLD2P4 and to apply it within a PSBLAS Krylov solver.
-On the other hand, the routines of the middle and lower layer can be used and extended
-by expert users to build new versions of multi-level Schwarz preconditioners.\\
-
-\textbf{Organizzazione della guida:\\
-dire che per il momento non
-forniamo anche la documentazione del middle layer, ma lo faremo in seguito\\}
-
-\textbf{Evidenziare le parole chiave che caratterizzano il nostro package}
-
-%%% Local Variables: 
-%%% mode: latex
-%%% TeX-master: "userguide"
-%%% End: 
+\section{General Overview\label{sec:overview}}
+
+The \emph{Multi-Level Domain Decomposition Parallel Preconditioners Package based on
+PSBLAS (MLD2P4}) provides various versions of multi-level Schwarz preconditioners~\cite{DD2},
+to be used in the iterative solutions of sparse linear systems $Ax=b$, where
+$A$ is a square, real or complex, sparse matrix with a symmetric sparsity pattern.
+\textbf{Ma non abbiamo detto che, se il pattern di sparista' non e' simmetrico,
+lavoriamo su $(A+A^T)/2$? Ma questo vale solo per l'aggregazione? Dovremmo fare
+qualcosa di consistente anche con 1-lev Schwarz.}
+Both additive and hybrid preconditioners, i.e.\ multiplicative among the levels
+and additive inside a level, are implemented; the basic additive Schwarz preconditioners
+are obtained by considering only one level. A purely algebraic approach is used to
+generate a sequence of coarse-level corrections to a basic preconditioner, without
+explicitly using any information on the geometry of the original problem (e.g.\ the
+discretization of a PDE). The smoothed aggregation technique is applied
+as algebraic coarsening strategy~\cite{}.
+
+The package is written in Fortran~95, using object-oriented techniques,
+and is based on a distributed-memory parallel programming paradigm. \textbf{SALVATORE,
+potresti aggiungere due righe sulla scelta del Fortran 95 e sul semplice interfacciamento
+con i legacy codes, senza ripetere quello che e' detto sotto sulla scelta di PSBLAS?}
+Single and double precision implementations of MLD2P4 are available for both the
+real and the complex case, that can be used through a single interface.
+\textbf{SALVATORE, funziona tutto?}
+
+MLD2P4 has been designed to implement scalable and easy-to-use multilevel preconditioners
+in the context of the PSBLAS (Parallel Sparse BLAS) computational framework~\cite{}.
+PSBLAS is a library originally developed to address the parallel implementation of
+iterative solvers for sparse linear system, by providing basic linear algebra
+operators and data management facilities for distributed sparse matrices; it
+also includes parallel Krylov solvers, built on the top of the basic PSBLAS kernels.
+The preconditioners available in MLD2P4 can be used with these Krylov solvers.
+The choice of PSBLAS has been mainly motivated by the need of having
+a portable and efficient software infrastructure implementing ``de facto'' standard
+parallel sparse linear algebra kernels, to pursue goals such as performance,
+portability, modularity ed extensibility in the development of the preconditioner
+package. On the other hand, the implementation of MLD2P4 has led to some
+revisions and extentions of the PSBLAS kernels, leading to the
+recent PSBLAS 2.0 version~\cite{}. The inter-process comunication required
+by MLD2P4 is encapsulated into the PSBLAS routines, except few cases where
+MPI~\cite{} is explicitly called. Therefore, MLD2P4 can be run on any parallel
+machine where PSBLAS and MPI implementations are available.
+
+MLD2P4 has a layered and modular software architecture where three main layers can be identified. The lower layer consists of the PSBLAS kernels, the middle one implements
+the construction and application phases of the preconditioners, and the upper one
+provides a uniform and easy-to-use interface to all the preconditioners. 
+This architecture allows for different levels of use of the package:
+few black-box routines at the upper level allow non-expert users to easily
+build any preconditioner available in MLD2P4 and to apply it within a PSBLAS Krylov solver.
+On the other hand, the routines of the middle and lower layer can be used and extended
+by expert users to build new versions of multi-level Schwarz preconditioners.\\
+
+\textbf{Organizzazione della guida:\\
+dire che per il momento non
+forniamo anche la documentazione del middle layer, ma lo faremo in seguito\\}
+
+\textbf{Evidenziare le parole chiave che caratterizzano il nostro package}
+
+%%% Local Variables: 
+%%% mode: latex
+%%% TeX-master: "userguide"
+%%% End: 
diff --git a/docs/pdf/title.tex b/docs/pdf/title.tex
index 89b9ec82..a685f23f 100644
--- a/docs/pdf/title.tex
+++ b/docs/pdf/title.tex
@@ -5,37 +5,46 @@
 
 \ifx\pdfoutput\undefined % We're not running pdftex
 \else
-\pdfbookmark{MLD2P4-1.0 User's Guide}{title}
+\pdfbookmark{MLD2P4 User's and Reference Guide}{title}
 \fi
-\newlength{\centeroffset}
-\setlength{\centeroffset}{-0.5\oddsidemargin}
-\addtolength{\centeroffset}{0.5\evensidemargin}
+%\newlength{\centeroffset}
+%\setlength{\centeroffset}{-0.5\oddsidemargin}
+%\addtolength{\centeroffset}{0.5\evensidemargin}
 %\addtolength{\textwidth}{-\centeroffset}
 \thispagestyle{empty}
 \vspace*{\stretch{1}}
 \noindent\hspace*{\centeroffset}\makebox[0pt][l]{\begin{minipage}{\textwidth}
 \flushright
-{\Huge\bfseries MLD2P4-1.0 User's guide
+{\Huge\bfseries MLD2P4\\[.8ex] User's and Reference Guide
 }
 \noindent\rule[-1ex]{\textwidth}{5pt}\\[2.5ex]
-\hfill\emph{\Large A reference guide for the MultiLevel Domain
-  Decomposition Parallel Preconditioners Package based on Parallel Sparse BLAS}
+\hfill\emph{\Large A guide for the Multi-Level Domain Decomposition \\[.6ex]
+Parallel Preconditioners Package
+based on PSBLAS}
+\end{minipage}}
+
+
+\vspace{\stretch{1}}
+\noindent\hspace*{\centeroffset}\makebox[0pt][l]{\begin{minipage}{\textwidth}
+\flushright
+{\large\bfseries Pasqua D'Ambra}\\
+\large ICAR-CNR, Naples, Italy\\[3ex]
+{\large\bfseries Daniela di Serafino}\\
+\large Second University of Naples, Italy\\[3ex]
+{\large\bfseries Salvatore Filippone} \\
+\large University of Rome ``Tor Vergata'', Italy 
+%\\[10ex]
+%\today
 \end{minipage}}
 
 \vspace{\stretch{1}}
 \noindent\hspace*{\centeroffset}\makebox[0pt][l]{\begin{minipage}{\textwidth}
 \flushright
-{\bfseries 
-by Salvatore Filippone\\
-   Alfredo Buttari} \\
-University of Rome ``Tor Vergata'' \\[3ex]
-{\bfseries Daniela di Serafino }\\
-Second University of Naples\\[3ex]
-{\bfseries Pasqua D'Ambra}\\
-ICAR-CNR, Naples\\[3ex]
+\large Software version: 1.0\\
 \today
 \end{minipage}}
 
+
 %\addtolength{\textwidth}{\centeroffset}
 \vspace{\stretch{2}}
 
@@ -48,4 +57,3 @@ ICAR-CNR, Naples\\[3ex]
 % mode: latex
 % mode: flyspell
 % End:
-
diff --git a/docs/pdf/userguide.tex b/docs/pdf/userguide.tex
index 3ac58b0c..9fc49cd6 100644
--- a/docs/pdf/userguide.tex
+++ b/docs/pdf/userguide.tex
@@ -35,6 +35,14 @@
 %  /URI (http://ce.uniroma2.it/psblas)
 } 
 
+\setlength\oddsidemargin{.7in}
+\setlength\evensidemargin{.7in}
+\newlength{\centeroffset}
+\setlength{\centeroffset}{0.5\oddsidemargin}
+\addtolength{\centeroffset}{0.5\evensidemargin}
+\addtolength{\textwidth}{-\centeroffset}
+\pagestyle{myheadings}
+
 \newcounter{subroutine}[subsection]
 \newcounter{example}[subroutine]
 \makeatletter
diff --git a/docs/userguide.pdf b/docs/userguide.pdf
index 07569223..1b1c4a22 100644
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Td[(b)28(y)-305(consid)1(e)-1(ri)1(ng)-305(on)1(ly)-305(one)-305(lev)28(e)-1(l.)-434(A)-305(pu)1(re)-1(l)1(y)-305(algebrai)1(c)-306(app)1(roac)28(h)-305(is)-305(use)-1(d)-304(to)-305(ge)-1(n)1(e)-1(r)1(-)]TJ 0 -13.5492 Td[(ate)-323(a)-323(se)-1(q)1(uence)-324(of)-322(coars)-1(e-le)-1(v)28(el)-322(c)-1(orr)1(e)-1(ction)1(s)-324(t)1(o)-323(a)-323(b)1(as)-1(ic)-323(p)1(re)-1(cond)1(ition)1(e)-1(r)1(,)-325(with)1(out)]TJ 0 -13.5492 Td[(expli)1(c)-1(it)1(ly)-444(using)-444(an)28(y)-444(in)1(for)1(m)-1(ati)1(on)-444(on)-444(the)-444(ge)-1(ome)-1(tr)1(y)-444(of)-444(the)-444(origin)1(al)-444(prob)1(lem)]TJ 0 -13.5492 Td[(\050e.g.)-384(th)1(e)-385(d)1(is)-1(cretization)-384(of)-383(a)-384(PDE)1(\051.)-384(The)-384(s)-1(mo)-28(oth)1(e)-1(d)-383(aggregation)-384(tec)27(h)1(niq)1(ue)-385(i)1(s)]TJ 0 -13.5492 Td[(app)1(lied)-333(as)-334(algebr)1(aic)-334(coarse)-1(n)1(ing)-333(strategy)-333([].)]TJ 16.9365 -14.1048 Td[(The)-364(pac)28(k)55(age)-364(is)-364(writt)1(e)-1(n)-363(in)-364(F)84(ortr)1(an)-364(95,)-371(u)1(s)-1(in)1(g)-364(ob)-55(jec)-1(t-ori)1(e)-1(n)28(t)1(e)-1(d)-363(te)-1(c)28(hn)1(iques,)]TJ -16.9365 -13.5492 Td[(and)-221(is)-223(b)1(as)-1(ed)-222(on)-222(a)-222(di)1(s)-1(tr)1(ibu)1(te)-1(d)1(-m)-1(em)-1(or)1(y)-222(par)1(allel)-222(progr)1(am)-1(min)1(g)-223(p)1(arad)1(igm.)]TJ/F39 10.9091 Tf 333.5964 0 Td[(SAL-)]TJ -333.5964 -13.5492 Td[(V)127(A)96(TOR)-1(E)1(,)-285(p)-32(otres)1(t)-1(i)-284(a)-1(ggiunger)1(e)-285(due)-284(righe)-285(s)1(ul)-1(la)-284(scel)-1(ta)-284(del)-285(F)96(ortr)1(an)-285(95)]TJ 0 -13.5492 Td[(e)-392(s)1(ul)-392(sempl)-1(ice)-392(in)32(t)-1(er)1(f)-1(acciam)-1(en)32(to)-392(con)-391(i)-392(l)-1(egacy)-392(co)-32(des)1(,)-394(senza)-392(r)1(i)-1(p)-32(etere)]TJ 0 -13.5492 Td[(quell)-1(o)-386(c)31(h)1(e)-387(e')-387(dett)-1(o)-386(sotto)-387(su)1(l)-1(la)-387(scelta)-387(di)-387(PSBLAS?)]TJ/F15 10.9091 Tf 273.7442 0 Td[(Si)1(ngle)-336(and)-336(d)1(oub)1(le)]TJ -273.7442 -13.5492 Td[(pr)1(e)-1(cision)-245(implem)-1(en)28(tati)1(ons)-246(of)-245(MLD2P)1(4)-246(ar)1(e)-247(a)28(v)56(ailab)1(le)-246(f)1(or)-246(b)-27(oth)-245(the)-246(r)1(e)-1(al)-245(and)-245(th)1(e)]TJ 0 -13.5492 Td[(com)-1(p)1(le)-1(x)-320(c)-1(ase)-1(,)-323(th)1(at)-321(c)-1(an)-320(b)-28(e)-321(use)-1(d)-320(thr)1(ough)-321(a)-321(sin)1(gle)-322(in)29(te)-1(r)1(face)-1(.)]TJ/F39 10.9091 Tf 280.2314 0 Td[(SAL)128(V)127(A)96(TOR)-1(E)1(,)]TJ -280.2314 -13.5492 Td[(funzi)-1(ona)-383(tutto?)]TJ/F15 10.9091 Tf 16.9365 -14.1048 Td[(MLD2P)1(4)-319(h)1(as)-319(b)-27(e)-1(en)-318(des)-1(i)1(gned)-318(to)-319(i)1(m)-1(p)1(le)-1(men)28(t)-318(s)-1(calabl)1(e)-319(and)-318(eas)-1(y-to-use)-319(m)27(u)1(l-)]TJ -16.9365 -13.5492 Td[(til)1(e)-1(v)28(el)-249(prec)-1(on)1(di)1(tioners)-250(i)1(n)-249(the)-250(con)28(text)-249(of)-249(th)1(e)-250(PS)1(B)-1(LAS)-248(\050P)28(arall)1(e)-1(l)-249(S)1(parse)-250(BLAS\051)]TJ 0 -13.5492 Td[(com)-1(p)1(utati)1(onal)-236(fr)1(am)-1(ew)28(ork)-236([].)-411(PSBLAS)-236(i)1(s)-237(a)-236(lib)1(rary)-236(or)1(igin)1(ally)-236(dev)28(elop)-28(ed)-236(to)-236(ad)1(-)]TJ 0 -13.5492 Td[(dr)1(e)-1(ss)-237(the)-237(par)1(allel)-237(impl)1(e)-1(me)-1(n)29(tation)-236(of)-237(it)1(e)-1(rat)1(iv)28(e)-237(s)-1(olv)28(ers)-237(for)-236(s)-1(p)1(arse)-238(l)1(inear)-237(syste)-1(m,)]TJ 0 -13.5492 Td[(b)28(y)-350(p)1(ro)28(vid)1(ing)-350(b)1(as)-1(ic)-350(lin)1(e)-1(ar)-350(al)1(ge)-1(b)1(ra)-350(op)-28(erator)1(s)-351(an)1(d)-350(data)-350(managem)-1(en)28(t)-350(f)1(ac)-1(il)1(ities)]TJ 0 -13.5492 Td[(for)-295(distri)1(bu)1(te)-1(d)-295(s)-1(p)1(arse)-297(matri)1(c)-1(es)-1(;)-308(it)-296(al)1(s)-1(o)-296(in)1(c)-1(l)1(ud)1(e)-1(s)-296(par)1(allel)-296(Kry)1(lo)28(v)-296(s)-1(ol)1(v)28(e)-1(rs,)-303(bu)1(ilt)]TJ 0 -13.5492 Td[(on)-385(t)1(he)-385(top)-385(of)-384(the)-385(basic)-385(PS)1(B)-1(LAS)-384(k)28(e)-1(r)1(nels)-1(.)-599(Th)1(e)-386(p)1(re)-1(cond)1(ition)1(e)-1(r)1(s)-386(a)28(v)56(ailab)1(le)-385(in)]TJ 0 -13.5492 Td[(MLD2P)1(4)-288(can)-287(b)-28(e)-288(u)1(s)-1(ed)-288(wit)1(h)-288(th)1(e)-1(se)-288(Kr)1(ylo)28(v)-288(solv)28(ers.)-429(T)-1(h)1(e)-288(c)27(hoi)1(c)-1(e)-288(of)-287(PS)1(B)-1(LAS)-287(h)1(as)]TJ 0 -13.5492 Td[(b)-27(e)-1(en)-361(m)-1(ain)1(ly)-361(m)-1(oti)1(v)55(ated)-361(b)28(y)-362(t)1(he)-362(nee)-1(d)-361(of)-361(ha)28(vi)1(ng)-362(a)-361(p)-28(or)1(table)-362(an)1(d)-362(e\016c)-1(ien)28(t)-361(s)-1(oft)1(-)]TJ 0 -13.5492 Td[(w)28(are)-327(in)1(fr)1(as)-1(tr)1(uctur)1(e)-327(impleme)-1(n)28(ti)1(ng)-326(\134de)-326(facto")-327(stan)1(dard)-325(paral)1(le)-1(l)-326(spar)1(s)-1(e)-326(linear)]TJ 0 -13.5492 Td[(algebr)1(a)-254(k)28(ernels,)-270(t)1(o)-254(p)1(ursue)-254(goal)1(s)-254(s)-1(u)1(c)27(h)-253(as)-254(p)-27(e)-1(rf)1(ormance)-1(,)-269(p)-27(ortab)1(ilit)28(y)84(,)-269(m)-1(o)-27(dul)1(arit)28(y)]TJ 0 -13.5492 Td[(ed)-380(exte)-1(n)1(s)-1(i)1(bil)1(it)28(y)-380(in)-379(the)-380(dev)28(e)-1(lop)1(me)-1(n)28(t)-380(of)-379(the)-380(pr)1(e)-1(cond)1(ition)1(e)-1(r)-379(pac)27(k)56(age.)-584(On)-380(th)1(e)]TJ 0 -13.5492 Td[(oth)1(e)-1(r)-363(h)1(and)1(,)-371(th)1(e)-364(i)1(m)-1(p)1(le)-1(men)28(tation)-362(of)-363(MLD2P)1(4)-363(has)-363(le)-1(d)-362(to)-363(s)-1(ome)-364(r)1(e)-1(v)1(is)-1(i)1(ons)-364(an)1(d)]TJ 0 -13.5492 Td[(exte)-1(n)29(tions)-382(of)-382(the)-383(P)1(SBLAS)-382(k)28(ernels,)-395(l)1(e)-1(ad)1(ing)-382(to)-382(the)-383(r)1(e)-1(ce)-1(n)28(t)-382(P)1(SBLAS)-382(2.0)-382(v)28(e)-1(r)1(-)]TJ 0 -13.5492 Td[(sion)-242([].)-413(T)-1(h)1(e)-243(in)29(te)-1(r)1(-)-1(p)1(ro)-28(ce)-1(ss)-243(com)27(u)1(nication)-241(re)-1(q)1(uir)1(e)-1(d)-242(b)29(y)-242(MLD2P)1(4)-243(i)1(s)-243(encapsulated)]TJ 0 -13.5492 Td[(in)28(t)1(o)-262(the)-262(P)1(SBLAS)-261(rout)1(ines)-1(,)-275(e)-1(xce)-1(p)1(t)-262(f)1(e)-1(w)-262(case)-1(s)-262(where)-262(MP)1(I)-262([])-261(is)-262(e)-1(x)1(plicitl)1(y)-262(called.)]TJ 0 -13.5492 Td[(Therefore,)-278(M)1(LD2P4)-264(can)-264(b)-27(e)-265(r)1(un)-264(on)-263(an)28(y)-264(p)1(arallel)-264(mac)27(h)1(ine)-264(where)-265(P)1(SBLAS)-264(an)1(d)]TJ 0 -13.5492 Td[(MP)1(I)-334(i)1(m)-1(p)1(le)-1(men)28(tation)1(s)-334(are)-333(a)27(v)56(ail)1(able.)]TJ 16.9365 -14.1048 Td[(MLD2P)1(4)-386(has)-386(a)-386(la)28(y)28(e)-1(r)1(e)-1(d)-385(and)-385(m)-1(o)-28(d)1(ul)1(ar)-386(s)-1(of)1(t)28(w)27(ar)1(e)-387(ar)1(c)27(hi)1(te)-1(ctur)1(e)-387(where)-386(thr)1(e)-1(e)]TJ
+/F15 10.9091 Tf 425.2005 740.0018 Td[(1)]TJ
 ET
-1 0 0 1 93.9178 91.633 cm
+1 0 0 1 430.655 740.0018 cm
 0 g 0 G
-1 0 0 1 -93.9178 -91.633 cm
+1 0 0 1 -430.655 -740.0018 cm
 BT
-/F15 10.9091 Tf 270.5181 91.633 Td[(1)]TJ
+/F19 14.3462 Tf 122.3998 704.1363 Td[(1)-1125(G)-1(ener)-1(al)-375(Ov)31(ervi)-1(ew)]TJ/F15 10.9091 Tf 0 -25.7054 Td[(The)]TJ/F42 10.9091 Tf 22.4222 0 Td[(Mu)1(lti-L)51(evel)-357(Domai)1(n)-358(De)51(c)51(omp)51(ositi)1(o)-1(n)-357(P)-1(ar)52(al)-51(lel)-357(Pr)51(e)51(c)51(onditi)1(o)-1(ner)1(s)]TJ -22.4222 -13.5492 Td[(Packa)-1(ge)-358(b)51(ase)51(d)-358(on)-359(PSBLAS)-359(\050MLD2P4)]TJ/F15 10.9091 Tf 182.147 0 Td[(\051)-334(p)1(ro)28(vid)1(e)-1(s)-334(v)56(ariou)1(s)-335(v)28(ersion)1(s)]TJ -182.147 -13.5492 Td[(of)-284(m)27(ul)1(ti-le)-1(v)28(el)-285(S)1(c)27(h)28(w)28(arz)-285(pr)1(e)-1(cond)1(ition)1(e)-1(r)1(s)-286([)]TJ/F41 10.9091 Tf 185.6113 0 Td[(?)]TJ/F15 10.9091 Tf 5.9242 0 Td[(],)-294(to)-285(b)-27(e)-285(use)-1(d)-284(in)-284(the)-285(itera-)]TJ -191.5355 -13.5492 Td[(tiv)28(e)-231(solu)1(tions)-231(of)-230(spar)1(s)-1(e)-231(l)1(inear)-230(s)-1(ystem)-1(s)]TJ/F11 10.9091 Tf 176.1781 0 Td[(Ax)]TJ/F15 10.9091 Tf 17.4469 0 Td[(=)]TJ/F11 10.9091 Tf 11.5151 0 Td[(b)]TJ/F15 10.9091 Tf 4.6818 0 Td[(,)-251(where)]TJ/F11 10.9091 Tf 36.1928 0 Td[(A)]TJ/F15 10.9091 Tf 10.6963 0 Td[(is)-231(a)-230(s)-1(q)1(uare,)]TJ -256.7111 -13.5492 Td[(real)-265(or)-266(com)-1(p)1(lex,)-279(sparse)-266(m)-1(at)1(rix)-265(with)-265(a)-266(symm)-1(etric)-266(spar)1(s)-1(i)1(t)27(y)-265(pat)1(te)-1(r)1(n.)]TJ/F41 10.9091 Tf 0 -13.5492 Td[(Ma)-351(non)-351(abbiamo)-352(d)1(e)-1(tto)-351(c)32(he,)-358(se)-351(i)-1(l)-351(patt)-1(er)1(n)-351(di)-352(sp)1(arista')-352(non)]TJ 0 -13.5492 Td[(e')-409(sim)-1(metric)-1(o,)-415(l)-1(a)32(v)32(or)1(i)-1(amo)-409(su)]TJ/F15 10.9091 Tf 156.2761 0 Td[(\050)]TJ/F11 10.9091 Tf 4.2425 0 Td[(A)]TJ/F15 10.9091 Tf 10.7674 0 Td[(+)]TJ/F11 10.9091 Tf 11.0704 0 Td[(A)]TJ/F25 7.9701 Tf 8.1818 3.9588 Td[(T)]TJ/F15 10.9091 Tf 6.6045 -3.9588 Td[(\051)]TJ/F11 10.9091 Tf 4.2425 0 Td[(=)]TJ/F15 10.9091 Tf 5.4545 0 Td[(2)]TJ/F41 10.9091 Tf 5.4546 0 Td[(?)-588(M)1(a)-409(questo)-409(v)64(ale)]TJ -212.2943 -13.5492 Td[(solo)-309(p)-32(er)-308(l)-1('aggregazi)-1(on)1(e)-1(?)-486(Do)32(vr)1(e)-1(mmo)-309(f)-1(ar)1(e)-309(qualc)-1(os)1(a)-309(di)-309(c)-1(on)1(-)]TJ 0 -13.5492 Td[(sisten)32(te)-387(anc)32(he)-386(c)-1(on)-386(1-l)-1(ev)-386(Sc)32(h)32(w)32(arz.)]TJ/F15 10.9091 Tf 187.0711 0 Td[(Both)-336(add)1(itiv)28(e)-336(and)-335(h)28(ybr)1(id)]TJ -187.0711 -13.5492 Td[(pr)1(e)-1(cond)1(ition)1(e)-1(r)1(s)-1(,)-332(i.)1(e)-1(.)-331(m)27(u)1(ltip)1(licativ)28(e)-332(am)-1(on)1(g)-332(the)-332(lev)28(e)-1(l)1(s)-333(an)1(d)-332(ad)1(diti)1(v)28(e)]TJ 0 -13.5492 Td[(in)1(s)-1(id)1(e)-387(a)-386(lev)28(e)-1(l)1(,)-399(are)-387(imp)1(le)-1(men)28(te)-1(d)1(;)-412(the)-386(basic)-387(ad)1(diti)1(v)28(e)-387(Sc)28(h)28(w)28(arz)-387(p)1(re-)]TJ 0 -13.5492 Td[(condi)1(tioners)-298(are)-299(ob)1(tain)1(e)-1(d)-297(b)28(y)-298(c)-1(on)1(s)-1(i)1(derin)1(g)-299(on)1(ly)-298(on)1(e)-299(lev)28(e)-1(l)1(.)-433(A)-298(pu)1(rely)]TJ 0 -13.5492 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+/F19 14.3462 Tf 122.3998 704.1363 Td[(5)-1125(G)-1(et)-1(ti)-1(ng)-375(St)-1(a)1(r)-1(te)-1(d)]TJ/F15 10.9091 Tf 0 -25.7328 Td[(W)84(e)-383(des)-1(crib)-27(e)-383(the)-382(basic)-1(s)-383(f)1(or)-382(bui)1(ldi)1(ng)-383(an)1(d)-382(app)1(lyin)1(g)-383(M)1(LD2P4)-382(one-)]TJ 0 -13.5492 Td[(lev)28(e)-1(l)-514(an)1(d)-514(m)27(ul)1(ti-le)-1(v)28(el)-514(Sc)28(h)28(w)27(ar)1(z)-515(pr)1(e)-1(cond)1(ition)1(e)-1(rs)-514(w)-1(i)1(th)-514(the)-515(Kr)1(ylo)28(v)]TJ 0 -13.5492 Td[(solv)28(e)-1(r)1(s)-334(in)1(c)-1(lu)1(ded)-333(in)-333(P)1(SBLAS)-333([].)-444(The)-333(follo)28(win)1(g)-334(steps)-334(ar)1(e)-334(requi)1(re)-1(d)1(:)]TJ
+ET
+1 0 0 1 122.3998 625.9473 cm
 0 g 0 G
-1 0 0 1 358.655 0 cm
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+BT
+/F15 10.9091 Tf 135.7332 625.9473 Td[(1.)]TJ
+ET
+1 0 0 1 144.218 625.9473 cm
 0 g 0 G
-1 0 0 1 -500.3935 -740.0018 cm
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 BT
-/F19 14.3462 Tf 141.7385 704.1363 Td[(5)-1125(G)-1(et)-1(ti)-1(ng)-375(St)-1(a)1(r)-1(te)-1(d)]TJ/F15 10.9091 Tf 0 -24.3522 Td[(W)84(e)-452(d)1(e)-1(sc)-1(r)1(ib)-27(e)-451(the)-451(basics)-451(for)-450(bui)1(ldi)1(ng)-451(an)1(d)-451(ap)1(pl)1(ying)-450(MLD2P)1(4)-451(one-le)-1(v)28(el)-451(an)1(d)]TJ 0 -13.5492 Td[(m)27(u)1(lti-lev)28(e)-1(l)-311(Sc)28(h)28(w)28(arz)-312(pr)1(e)-1(cond)1(ition)1(e)-1(r)1(s)-313(wit)1(h)-312(t)1(he)-312(Kry)1(lo)28(v)-312(solv)28(ers)-312(in)1(c)-1(lu)1(ded)-311(in)-311(PS)1(-)]TJ 0 -13.5492 Td[(BLAS)-333([].)-444(The)-334(f)1(ollo)28(win)1(g)-334(\014)1(v)28(e)-334(s)-1(t)1(e)-1(p)1(s)-334(are)-334(r)1(e)-1(qu)1(ired:)]TJ
+/F42 10.9091 Tf 149.6726 625.9473 Td[(De)51(cl)1(a)-1(r)52(e)-460(t)-1(he)-460(pr)51(e)51(c)52(o)-1(ndi)1(t)-1(i)1(on)-1(er)-460(data)-460(st)-1(r)1(uctur)52(e)]TJ/F15 10.9091 Tf 199.3562 0 Td[(.)-778(I)-1(t)-444(is)-445(a)-445(deri)1(v)28(e)-1(d)]TJ -199.3562 -13.5492 Td[(dat)1(a)-405(t)28(yp)-28(e,)]TJ/F55 10.9091 Tf 54.1796 0 Td[(mld_)]TJ/F42 10.9091 Tf 22.9088 0 Td[(x)]TJ/F55 10.9091 Tf 6.3742 0 Td[(prec_type)]TJ/F15 10.9091 Tf 51.5449 0 Td[(,where)]TJ/F42 10.9091 Tf 35.3559 0 Td[(x)]TJ/F15 10.9091 Tf 10.7907 0 Td[(ma)27(y)-404(b)-28(e)]TJ/F55 10.9091 Tf 40.0452 0 Td[(s)]TJ/F15 10.9091 Tf 5.7272 0 Td[(,)]TJ/F55 10.9091 Tf 7.6418 0 Td[(d)]TJ/F15 10.9091 Tf 5.7272 0 Td[(,)]TJ/F55 10.9091 Tf 7.6419 0 Td[(c)]TJ/F15 10.9091 Tf 10.1437 0 Td[(or)]TJ/F55 10.9091 Tf 14.1438 0 Td[(z)]TJ/F15 10.9091 Tf 5.7272 0 Td[(,)]TJ -277.9522 -13.5492 Td[(acc)-1(ord)1(in)1(g)-345(to)-344(the)-345(b)1(as)-1(ic)-345(d)1(ata)-345(t)28(yp)-27(e)-345(of)-344(th)1(e)-345(s)-1(p)1(ars)-1(e)-345(matr)1(ix)-345(\050)]TJ/F55 10.9091 Tf 263.0117 0 Td[(s)]TJ/F15 10.9091 Tf 9.4859 0 Td[(=)]TJ -272.4976 -13.5492 Td[(real)-272(single)-272(pr)1(e)-1(cis)-1(i)1(on;)]TJ/F55 10.9091 Tf 98.402 0 Td[(s)]TJ/F15 10.9091 Tf 8.6961 0 Td[(=)-272(real)-272(dou)1(bl)1(e)-273(pr)1(e)-1(cision;)]TJ/F55 10.9091 Tf 114.6436 0 Td[(c)]TJ/F15 10.9091 Tf 8.6961 0 Td[(=)-272(com)-1(p)1(lex)]TJ -230.4378 -13.5492 Td[(single)-355(prec)-1(i)1(s)-1(ion)1(;)]TJ/F55 10.9091 Tf 79.5414 0 Td[(z)]TJ/F15 10.9091 Tf 9.6043 0 Td[(=)-355(c)-1(ompl)1(e)-1(x)-355(d)1(oubl)1(e)-356(pr)1(e)-1(cis)-1(i)1(on\051.)-510(This)-356(d)1(ata)]TJ -89.1456 -13.5492 Td[(structu)1(re)-289(i)1(s)-289(acc)-1(es)-1(se)-1(d)-287(b)28(y)-288(th)1(e)-289(u)1(s)-1(er)-288(onl)1(y)-288(thr)1(ough)-288(th)1(e)-289(M)1(LD2P4)]TJ 0 -13.5492 Td[(rou)1(tin)1(e)-1(s,)-333(follo)28(win)1(g)-334(an)-333(ob)-55(j)1(e)-1(ct-orien)28(ted)-333(app)1(roac)27(h)1(.)]TJ
 ET
-1 0 0 1 141.7385 631.7579 cm
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 0 g 0 G
-1 0 0 1 -141.7385 -631.7579 cm
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 BT
-/F15 10.9091 Tf 155.0719 631.7579 Td[(1.)]TJ
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 ET
-1 0 0 1 163.5567 631.7579 cm
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 0 g 0 G
-1 0 0 1 -163.5567 -631.7579 cm
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 BT
-/F41 10.9091 Tf 169.0113 631.7579 Td[(A)25(l)-50(lo)51(c)51(ate)-395(an)-1(d)-395(initi)1(a)-1(l)1(ize)-395(the)-395(pr)51(e)51(c)51(onditioner)-395(data)-396(str)1(uctur)52(e,)-405(ac)51(c)51(or)52(ding)-395(t)-1(o)]TJ 0 -13.5492 Td[(a)-449(pr)52(e)51(c)51(ond)-1(i)1(tioner)-449(ty)1(p)51(e)-449(chosen)-449(by)-448(the)-449(u)1(ser)]TJ/F15 10.9091 Tf 197.606 0 Td[(.)-740(This)-432(is)-432(p)-28(erf)1(orme)-1(d)-431(b)28(y)-432(th)1(e)]TJ -197.606 -13.5492 Td[(rou)1(tin)1(e)]TJ/F52 10.9091 Tf 39.1768 0 Td[(mld_precinit)]TJ/F15 10.9091 Tf 68.7265 0 Td[(,)-513(whic)28(h)-477(also)-478(se)-1(ts)-477(a)-478(d)1(e)-1(f)1(aul)1(t)-478(p)1(rec)-1(on)1(diti)1(oner)-477(for)]TJ -107.9033 -13.5492 Td[(eac)27(h)-449(p)1(rec)-1(on)1(dit)1(ioner)-449(t)28(yp)-27(e)-449(s)-1(elec)-1(ted)-449(b)29(y)-449(the)-449(u)1(s)-1(er.)-791(The)-449(defau)1(lt)-449(p)1(rec)-1(on)1(-)]TJ 0 -13.5492 Td[(di)1(tioner)-451(ass)-1(o)-28(ciated)-451(to)-451(e)-1(ac)28(h)-451(pr)1(e)-1(cond)1(ition)1(e)-1(r)-451(t)28(yp)-27(e)-452(i)1(s)-452(liste)-1(d)-450(in)-451(T)83(ab)1(le)]TJ
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 ET
-1 0 0 1 491.9087 577.5611 cm
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 0 0 1 rg 0 0 1 RG
-1 0 0 1 -491.9087 -577.5611 cm
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 BT
-/F15 10.9091 Tf 491.9087 577.5611 Td[(1)]TJ
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 ET
-1 0 0 1 497.3632 577.5611 cm
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 0 g 0 G
-1 0 0 1 -497.3632 -577.5611 cm
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 BT
-/F15 10.9091 Tf 497.3632 577.5611 Td[(;)]TJ -328.3519 -13.5492 Td[(th)1(e)-319(strin)1(g)-318(use)-1(d)-318(b)29(y)]TJ/F52 10.9091 Tf 89.1836 0 Td[(mld_precinit)]TJ/F15 10.9091 Tf 72.1967 0 Td[(to)-318(id)1(e)-1(n)28(t)1(ify)-318(eac)27(h)-317(prec)-1(on)1(di)1(tioner)-318(t)28(yp)-27(e)]TJ -161.3803 -13.5492 Td[(is)-413(also)-413(giv)28(en.)-682(Th)1(e)-414(p)1(rec)-1(on)1(dit)1(ioner)-412(data)-413(stru)1(c)-1(t)1(ure)-413(is)-413(th)1(e)-413(deriv)28(ed)-412(data)]TJ 0 -13.5492 Td[(t)28(yp)-27(e)]TJ/F52 10.9091 Tf 25.0145 0 Td[(mld_prec_type)]TJ/F15 10.9091 Tf 74.4537 0 Td[(,)-387(whi)1(c)27(h)-376(is)-376(ac)-1(ce)-1(ss)-1(ed)-376(to)-376(the)-376(use)-1(r)-376(on)1(ly)-376(thr)1(ough)-376(th)1(e)]TJ -99.4682 -13.5492 Td[(MLD2P)1(4)-333(routi)1(nes)-1(.)]TJ
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 ET
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 0 g 0 G
-1 0 0 1 -141.7385 -501.4838 cm
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 BT
-/F15 10.9091 Tf 155.0719 501.4838 Td[(2.)]TJ
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 ET
-1 0 0 1 163.5567 501.4838 cm
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 0 g 0 G
-1 0 0 1 -163.5567 -501.4838 cm
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 BT
-/F41 10.9091 Tf 169.0113 501.4838 Td[(Cho)51(ose)-450(a)-451(s)1(p)51(e)51(ci\014c)-451(var)1(iant)-451(of)-450(t)-1(he)-450(sel)1(e)51(ct)-1(e)52(d)-451(pr)51(e)51(c)52(o)-1(nditi)1(o)-1(ner)-450(typ)51(e,)-473(by)-450(set-)]TJ 0 -13.5492 Td[(ting)-388(the)-388(pr)51(e)51(c)51(onditioner)-388(p)51(ar)52(ameters.)]TJ/F15 10.9091 Tf 173.6233 0 Td[(This)-366(is)-366(p)-28(erf)1(orme)-1(d)-366(b)29(y)-366(the)-366(rout)1(ine)]TJ/F52 10.9091 Tf -173.6233 -13.5492 Td[(mld_precset)]TJ/F15 10.9091 Tf 62.9993 0 Td[(.)-430(A)-290(few)-291(e)-1(x)1(am)-1(p)1(le)-1(s)-291(concerni)1(ng)-291(t)1(he)-291(use)-291(of)]TJ/F52 10.9091 Tf 187.6382 0 Td[(mld_precset)]TJ/F15 10.9091 Tf 66.169 0 Td[(are)]TJ -316.8065 -13.5492 Td[(giv)28(en)-364(i)1(n)-364(Sections)]TJ/F39 10.9091 Tf 84.6979 0 Td[(??)]TJ/F15 10.9091 Tf 15.8183 0 Td[(and)]TJ/F39 10.9091 Tf 21.5458 0 Td[(??)]TJ/F15 10.9091 Tf 11.8484 0 Td[(;)-379(a)-364(com)-1(p)1(lete)-365(l)1(is)-1(t)-364(of)-363(all)-363(the)-364(pr)1(e)-1(cond)1(ition)1(e)-1(r)]TJ -133.9104 -13.5492 Td[(par)1(am)-1(eters)-334(an)1(d)-333(their)-333(all)1(o)27(w)28(e)-1(d)-332(v)55(al)1(ues)-334(is)-334(p)1(ro)28(vid)1(e)-1(d)-333(i)1(n)-333(Sec)-1(ti)1(on)]TJ
+/F42 10.9091 Tf 149.6726 399.092 Td[(Cho)51(ose)-366(a)-367(sp)51(e)52(ci\014c)-367(pr)52(e)51(c)51(on)-1(di)1(t)-1(i)1(on)-1(er)-366(within)-366(t)-1(he)-366(sele)51(cte)51(d)-366(pr)51(e)51(c)51(on-)]TJ 0 -13.5492 Td[(ditioner)-261(ty)1(p)51(e,)-281(by)-260(sett)-1(i)1(ng)-261(t)-1(he)-261(pr)51(e)52(c)51(on)-1(di)1(t)-1(i)1(on)-1(er)-260(p)51(ar)51(ameters.)]TJ/F15 10.9091 Tf 259.7097 0 Td[(This)]TJ -259.7097 -13.5492 Td[(is)-338(p)-27(e)-1(rf)1(orme)-1(d)-337(b)28(y)-337(the)-338(rout)1(ine)]TJ/F55 10.9091 Tf 134.9462 0 Td[(mld_precset)]TJ/F15 10.9091 Tf 62.9993 0 Td[(.)-458(A)-338(f)1(e)-1(w)-338(exam)-1(p)1(les)]TJ -197.9455 -13.5492 Td[(conce)-1(rn)1(in)1(g)-284(the)-284(u)1(s)-1(e)-284(of)]TJ/F55 10.9091 Tf 102.474 0 Td[(mld_precset)]TJ/F15 10.9091 Tf 66.0951 0 Td[(are)-284(giv)28(en)-283(in)-284(S)1(e)-1(ction)]TJ
 ET
-1 0 0 1 450.8297 447.287 cm
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 0 0 1 rg 0 0 1 RG
-1 0 0 1 -450.8297 -447.287 cm
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 BT
-/F15 10.9091 Tf 450.8297 447.287 Td[(6)]TJ
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 ET
-1 0 0 1 456.2843 447.287 cm
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 0 g 0 G
-1 0 0 1 -456.2843 -447.287 cm
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 BT
-/F15 10.9091 Tf 456.2843 447.287 Td[(.)]TJ
+/F15 10.9091 Tf 427.6247 358.4444 Td[(;)]TJ -277.9521 -13.5492 Td[(a)-505(com)-1(p)1(le)-1(t)1(e)-506(li)1(s)-1(t)-505(of)-504(all)-505(th)1(e)-506(p)1(rec)-1(on)1(diti)1(oner)-505(par)1(am)-1(ete)-1(r)1(s)-506(an)1(d)]TJ 0 -13.5492 Td[(th)1(e)-1(ir)-333(al)1(lo)28(w)27(ed)-333(v)56(alues)-334(is)-334(p)1(ro)28(vid)1(e)-1(d)-332(in)-333(Sec)-1(t)1(ion)]TJ
 ET
-1 0 0 1 141.7385 425.4065 cm
-0 g 0 G
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+0 0 1 rg 0 0 1 RG
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 BT
-/F15 10.9091 Tf 155.0719 425.4065 Td[(3.)]TJ
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 ET
-1 0 0 1 163.5567 425.4065 cm
+1 0 0 1 359.2485 331.346 cm
 0 g 0 G
-1 0 0 1 -163.5567 -425.4065 cm
+1 0 0 1 -359.2485 -331.346 cm
 BT
-/F41 10.9091 Tf 169.0113 425.4065 Td[(Bui)1(ld)-355(th)-1(e)-355(pr)51(e)51(c)52(o)-1(nditi)1(o)-1(ner)-355(f)1(o)-1(r)-355(a)-355(given)-355(mat)-1(r)1(ix.)]TJ/F15 10.9091 Tf 213.1309 0 Td[(This)-331(is)-331(p)-27(e)-1(r)1(for)1(m)-1(ed)-331(b)29(y)-331(th)1(e)]TJ -213.1309 -13.5492 Td[(rou)1(tin)1(e)]TJ/F52 10.9091 Tf 37.6061 0 Td[(mld_precbld)]TJ/F15 10.9091 Tf 62.9993 0 Td[(.)]TJ
+/F15 10.9091 Tf 359.2485 331.346 Td[(.)]TJ
 ET
-1 0 0 1 141.7385 389.9768 cm
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 0 g 0 G
-1 0 0 1 -141.7385 -389.9768 cm
+1 0 0 1 -122.3998 -305.9881 cm
 BT
-/F15 10.9091 Tf 155.0719 389.9768 Td[(4.)]TJ
+/F15 10.9091 Tf 135.7332 305.9881 Td[(4.)]TJ
 ET
-1 0 0 1 163.5567 389.9768 cm
+1 0 0 1 144.218 305.9881 cm
 0 g 0 G
-1 0 0 1 -163.5567 -389.9768 cm
+1 0 0 1 -144.218 -305.9881 cm
 BT
-/F41 10.9091 Tf 169.0113 389.9768 Td[(App)-1(l)1(y)-378(t)-1(he)-378(p)-1(r)52(e)51(c)51(onditioner)-379(at)-379(e)52(a)-1(ch)-378(iter)51(ation)-379(of)-378(a)-379(Kry)1(lov)-379(sol)1(ver.)]TJ/F15 10.9091 Tf 298.8913 0 Td[(This)-356(is)]TJ -298.8913 -13.5492 Td[(p)-27(e)-1(r)1(formed)-422(b)29(y)-422(th)1(e)-422(rou)1(tine)]TJ/F52 10.9091 Tf 127.5775 0 Td[(mld_precaply)]TJ/F15 10.9091 Tf 68.7265 0 Td[(.)-709(Wh)1(e)-1(n)-421(u)1(s)-1(in)1(g)-422(th)1(e)-422(PS)1(B)-1(LAS)]TJ -196.304 -13.5492 Td[(Kr)1(ylo)28(v)-393(solv)28(ers)-1(,)-407(th)1(is)-393(s)-1(tep)-392(is)-393(c)-1(ompletely)-393(tr)1(anspar)1(e)-1(n)28(t)-392(to)-393(th)1(e)-394(u)1(s)-1(er,)-407(s)-1(i)1(nce)]TJ/F52 10.9091 Tf 0 -13.5492 Td[(mld_precaply)]TJ/F15 10.9091 Tf 74.4072 0 Td[(is)-521(called)-521(b)29(y)-521(th)1(e)-522(P)1(SBLAS)-520(rou)1(tine)-521(imp)1(le)-1(men)28(tin)1(g)-521(the)]TJ -74.4072 -13.5492 Td[(Kr)1(ylo)28(v)-333(s)-1(olv)28(er)-333(\050)]TJ/F52 10.9091 Tf 71.3334 0 Td[(psb_krylov)]TJ/F15 10.9091 Tf 57.2721 0 Td[(\051.)]TJ
+/F42 10.9091 Tf 149.6726 305.9881 Td[(Bui)1(ld)-459(t)-1(he)-459(pr)51(e)51(c)51(onditioner)-459(for)-459(a)-460(gi)1(ven)-460(matri)1(x.)]TJ/F15 10.9091 Tf 223.5704 0 Td[(This)-444(is)-444(p)-27(e)-1(r)1(-)]TJ -223.5704 -13.5492 Td[(for)1(m)-1(ed)-333(b)28(y)-333(th)1(e)-334(rou)1(tin)1(e)]TJ/F55 10.9091 Tf 108.2425 0 Td[(mld_precbld)]TJ/F15 10.9091 Tf 62.9993 0 Td[(.)]TJ
 ET
-1 0 0 1 141.7385 313.8995 cm
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 0 g 0 G
-1 0 0 1 -141.7385 -313.8995 cm
+1 0 0 1 -122.3998 -267.081 cm
 BT
-/F15 10.9091 Tf 155.0719 313.8995 Td[(5.)]TJ
+/F15 10.9091 Tf 135.7332 267.081 Td[(5.)]TJ
 ET
-1 0 0 1 163.5567 313.8995 cm
+1 0 0 1 144.218 267.081 cm
 0 g 0 G
-1 0 0 1 -163.5567 -313.8995 cm
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 ET
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 BT
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 BT
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 BT
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-1 0 0 1 352.9477 268.5901 cm
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+/F15 9.9626 Tf 128.3774 706.7266 Td[(P)28(ar)1(am)-1(ete)-1(r)-8727(Allo)28(w)28(e)-1(d)-333(v)56(alu)1(e)-1(s)]TJ 0 -11.9551 Td[(\050)]TJ/F55 9.9626 Tf 7.1952 0 Td[(what)]TJ/F15 9.9626 Tf 20.9214 0 Td[(\051)-10064(\050)]TJ/F55 9.9626 Tf 111.3317 0 Td[(val)]TJ/F15 9.9626 Tf 15.691 0 Td[(\051)]TJ/F55 9.9626 Tf -155.1393 -11.9552 Td[(mld_coarse_mat_)]TJ/F15 9.9626 Tf 132.253 0 Td[('DIS)1(T)-1(R')1(,)-334(')1(REPL')]TJ 0 -11.9552 Td[(Coarse)-334(Matr)1(ix:)-444(di)1(s)-1(tr)1(ibu)1(te)-1(d)-333(or)-333(r)1(e)-1(p)1(licate)-1(d)]TJ/F55 9.9626 Tf -132.253 -11.9551 Td[(mld_coarse_solve_)]TJ/F15 9.9626 Tf 132.253 0 Td[('ILU',)-333('M)1(ILU',)-333('ILUT',)-333('SLU')1(,)-334(')1(UMF',)-333(S)1(LUDIST',)-333(BJA)28(C)-1(????)]TJ 0 -11.9552 Td[(Av)56(ailab)1(le)-334(Coarse)-334(solv)28(e)-1(r)1(.)]TJ 0 -11.9552 Td[(On)1(ly)-333(SLUDIS)1(T)-334(e)-334(BJA)28(C)-334(can)-333(b)-27(e)-334(use)-1(d)-333(wh)1(e)-1(n)-333(coarse)-334(matrix)-333(is)-333(distri)1(but)1(e)-1(d)]TJ/F55 9.9626 Tf -132.253 -11.9551 Td[(mld_coarse_BJAC_sweeps_)]TJ/F15 9.9626 Tf 132.253 0 Td[(\050NON)-333(V)111(A)-333(B)-1(E)1(NE)-333(mldcoarse)-1(sw)27(ee)-1(p)1(s)-1(\051)-333(n)28(u)1(m)27(b)-27(er)-333(of)-333(B)-1(l)1(o)-28(c)27(k-Jacobi)-333(sw)27(ee)-1(p)1(s)-334(when)-333(B)-1(J)1(A)27(C)-333(is)-334(u)1(s)-1(ed)-333(as)-334(coars)-1(est)-334(solv)28(er)]TJ/F55 9.9626 Tf -132.253 -11.9552 Td[(mld_coarse_fill_in_)]TJ/F15 9.9626 Tf 132.253 0 Td[(lev)28(e)-1(l)-333(of)-333(\014)1(ll-in)-333(in)-332(MILU)-334(an)1(d)-333(ILU)-334(f)1(ac)-1(t)1(orization)]TJ 0 -11.9552 Td[(E)-333(IL)-333(T)-1(HRE)1(SHOLD)-333(P)1(ER)-333(ILU)-1(T?)]TJ
 ET
-1 0 0 1 168.3992 600.3132 cm
+1 0 0 1 164.1182 577.0089 cm
 0 g 0 G
-1 0 0 1 -168.3992 -600.3132 cm
+1 0 0 1 -164.1182 -577.0089 cm
 BT
-/F15 10.9091 Tf 168.3992 600.3132 Td[(T)83(ab)1(le)-334(5:)-444(P)28(aramete)-1(r)1(s)-334(for)-333(S)1(c)27(h)28(w)28(arz)-334(smo)-28(other/p)1(rec)-1(on)1(diti)1(oner)-333(t)27(y)1(p)-28(e.)]TJ
+/F15 10.9091 Tf 164.1182 577.0089 Td[(T)83(ab)1(le)-334(4:)-444(P)28(aramete)-1(r)1(s)-334(for)-333(coarse)-1(st)-333(m)-1(atr)1(ix)-333(s)-1(ol)1(v)28(e)-1(r.)]TJ
 ET
-1 0 0 1 473.7328 600.3132 cm
+1 0 0 1 388.9366 577.0089 cm
 0 g 0 G
-1 0 0 1 -331.9943 -2.7273 cm
+1 0 0 1 -266.5368 0 cm
 0 g 0 G
-1 0 0 1 -141.7385 -597.5859 cm
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 BT
-/F15 10.9091 Tf 141.7385 566.7017 Td[(th)1(e)-308(coup)1(le)-307(of)-307(v)56(alu)1(e)-1(s)-307('HALO)1(')-307(an)1(d)-307('S)1(UM')-306(of)-307(th)1(e)-307(argumen)28(t)]TJ/F52 10.9091 Tf 271.2845 0 Td[(val)]TJ/F15 10.9091 Tf 17.1816 0 Td[(,)-312(f)1(or)-307(th)1(e)-308(v)56(alu)1(e)-1(s)]TJ/F52 10.9091 Tf -288.4661 -13.5492 Td[(mld_sub_restr_)]TJ/F15 10.9091 Tf 84.9152 0 Td[(and)]TJ/F52 10.9091 Tf 22.3101 0 Td[(mld_sub_prol_)]TJ/F15 10.9091 Tf 79.188 0 Td[(of)-434(t)1(he)-434(argumen)28(t)]TJ/F52 10.9091 Tf 83.3241 0 Td[(what)]TJ/F15 10.9091 Tf 22.9088 0 Td[(,)-459(resp)-28(ec)-1(ti)1(v)28(e)-1(ly)84(.)]TJ -292.6462 -13.5492 Td[(Wh)1(ile,)-425(the)-407(RAS)-406(m)-1(etho)-27(d)-407(corres)-1(p)-27(on)1(ds)-407(to)-407(th)1(e)-408(coup)1(le)-407(of)-407(v)56(alu)1(e)-1(s)-407('NONE)1(')-407(an)1(d)]TJ 0 -13.5492 Td[('S)1(UM')-399(and)-399(ASH)-399(m)-1(etho)-27(d)-400(corr)1(e)-1(sp)-28(on)1(ds)-400(to)-399(the)-400(coup)1(le)-400(of)-400(v)56(alu)1(e)-1(s)-400(')1(HALO')-400(an)1(d)]TJ 0 -13.5492 Td[('NONE)1('.)]TJ/F19 11.9552 Tf 0 -29.2128 Td[(6.)-1(2)-1125(Pre)-1(condi)-1(ti)-1(one)-1(r)-375(Appli)-1(ca)1(t)-1(io)-1(n)]TJ/F15 10.9091 Tf 0 -20.5946 Td[(On)1(c)-1(e)-240(the)-240(prec)-1(on)1(di)1(tioner)-240(h)1(as)-241(b)-27(e)-1(en)-240(bu)1(ilt,)-258(it)-240(ma)28(y)-240(b)-28(e)-240(app)1(lied)-240(at)-240(e)-1(ac)28(h)-240(iterati)1(on)-240(of)]TJ 0 -13.5492 Td[(a)-340(Kryl)1(o)27(v)-340(solv)28(er)-340(b)28(y)-340(c)-1(al)1(ling)-340(th)1(e)-341(rou)1(tin)1(e)]TJ/F52 10.9091 Tf 182.8063 0 Td[(mld_precaply)]TJ/F15 10.9091 Tf 72.4391 0 Td[(\050CAMBIARE)-340(NOME)]TJ -255.2454 -13.5492 Td[(R)28(OUTINE)-279(NEL)-279(SOFTW)112(AR)-1(E)-279(E)1(VIT)83(ANDO)-279(L'UNDE)1(R)-1(S)1(CORE\051,)-279(whose)-280(API)]TJ 0 -13.5492 Td[(is)-273(sho)28(wn)-272(in)-272(Figu)1(re)]TJ
+/F15 10.9091 Tf 122.3998 545.6795 Td[(par)1(am)-1(eters)-376(in)-375(ord)1(e)-1(r)-375(to)-376(c)28(ho)-28(ose)-376(the)-376(t)28(yp)-27(e)-376(of)-375(addi)1(tiv)28(e)-376(Sc)28(h)28(w)27(ar)1(z)-376(v)28(e)-1(r)1(-)]TJ 0 -13.5492 Td[(sion)-357(\050AS,RAS)1(,ASH\051,)-357(th)1(e)-358(n)28(um)28(b)-28(er)-357(of)-358(o)28(v)28(erlap)1(s)-358(as)-358(w)27(ell)-357(as)-358(the)-358(lo)-28(cal)]TJ 0 -13.5492 Td[(solv)28(e)-1(r)1(.)-462(All)-339(th)1(e)-340(p)1(arame)-1(ters)-339(are)-340(r)1(e)-1(p)-27(orted)-339(in)-338(T)83(able)]TJ
 ET
-1 0 0 1 230.2974 422.0499 cm
+1 0 0 1 356.37 518.5811 cm
 0 0 1 rg 0 0 1 RG
-1 0 0 1 -230.2974 -422.0499 cm
+1 0 0 1 -356.37 -518.5811 cm
 BT
-/F15 10.9091 Tf 230.2974 422.0499 Td[(5)]TJ
+/F15 10.9091 Tf 356.37 518.5811 Td[(6.1.1)]TJ
 ET
-1 0 0 1 235.752 422.0499 cm
+1 0 0 1 378.7943 518.5811 cm
 0 g 0 G
-1 0 0 1 -235.752 -422.0499 cm
+1 0 0 1 -378.7943 -518.5811 cm
 BT
-/F15 10.9091 Tf 235.752 422.0499 Td[(.)-424(This)-272(routi)1(ne)-273(com)-1(p)1(utes)]TJ/F11 10.9091 Tf 116.7285 0 Td[(y)]TJ/F15 10.9091 Tf 8.7701 0 Td[(=)]TJ/F11 10.9091 Tf 11.5151 0 Td[(op)]TJ/F15 10.9091 Tf 10.7765 0 Td[(\050)]TJ/F11 10.9091 Tf 4.2425 0 Td[(M)]TJ/F28 7.9701 Tf 11.7727 3.9588 Td[(\000)]TJ/F22 7.9701 Tf 6.5865 0 Td[(1)]TJ/F15 10.9091 Tf 4.7323 -3.9588 Td[(\051)]TJ/F11 10.9091 Tf 6.0606 0 Td[(x)]TJ/F15 10.9091 Tf 6.2348 0 Td[(,)-284(w)-1(h)1(e)-1(r)1(e)]TJ/F11 10.9091 Tf 37.0182 0 Td[(M)]TJ/F15 10.9091 Tf 14.7458 0 Td[(is)-273(th)1(e)]TJ -333.1971 -13.5492 Td[(pr)1(e)-1(v)1(iously)-400(b)1(uil)1(t)-400(precondi)1(tioner,)-416(s)-1(t)1(ore)-1(d)-399(in)-399(the)]TJ/F52 10.9091 Tf 222.3636 0 Td[(prec)]TJ/F15 10.9091 Tf 27.2725 0 Td[(dat)1(a)-400(s)-1(tr)1(ucture,)-416(and)]TJ/F11 10.9091 Tf 98.2424 0 Td[(op)]TJ/F15 10.9091 Tf -347.8785 -13.5492 Td[(denot)1(e)-1(s)-367(th)1(e)-367(m)-1(atr)1(ix)-366(its)-1(elf)-366(or)-366(its)-367(tr)1(ansp)-28(ose)-1(,)-374(ac)-1(cord)1(ing)-366(to)-367(th)1(e)-367(v)56(alue)-367(of)]TJ/F52 10.9091 Tf 326.9887 0 Td[(trans)]TJ/F15 10.9091 Tf 28.636 0 Td[(.)]TJ -355.6247 -13.5492 Td[(Note)-475(that)-474(this)-475(rou)1(tin)1(e)-476(is)-475(called)-475(with)1(in)-474(the)-475(PS)1(B)-1(LAS)1(-)-1(b)1(as)-1(ed)-474(Kryl)1(o)27(v)-474(s)-1(olv)28(er)]TJ 0 -13.5492 Td[(a)28(v)56(ailabl)1(e)-289(in)-287(the)-289(P)1(SBLAS)-288(l)1(ibr)1(ary)-288(\050se)-1(e)-288(the)-288(PSBLAS)-288(User's)-289(G)1(uid)1(e)-289(f)1(or)-288(details\051,)]TJ 0 -13.5492 Td[(th)1(e)-1(refor)1(e)-1(,)-427(the)-409(use)-410(of)-408(this)-409(rou)1(tine)-409(is)-409(ge)-1(n)1(e)-1(r)1(ally)-409(tr)1(ansparen)28(t)-409(to)-409(th)1(e)-410(M)1(LD2P4)]TJ 0 -13.5492 Td[(user.)]TJ
+/F15 10.9091 Tf 378.7943 518.5811 Td[(.)-462(Its)-339(w)27(or)1(th)]TJ
 ET
-1 0 0 1 141.7385 91.633 cm
+1 0 0 1 122.3998 504.0595 cm
 0 g 0 G
-1 0 0 1 -141.7385 -91.633 cm
+1 0 0 1 -122.3998 -504.0595 cm
 BT
-/F15 10.9091 Tf 315.6115 91.633 Td[(16)]TJ
+/F15 9.9626 Tf 128.3774 495.6909 Td[(P)28(ar)1(am)-1(ete)-1(r)-5052(Allo)28(w)28(e)-1(d)-333(v)56(alu)1(e)-1(s)]TJ 0 -11.9552 Td[(\050)]TJ/F55 9.9626 Tf 3.8744 0 Td[(what)]TJ/F15 9.9626 Tf 20.9213 0 Td[(\051)-6722(\050)]TJ/F55 9.9626 Tf 74.7193 0 Td[(val)]TJ/F15 9.9626 Tf 15.691 0 Td[(\051)]TJ/F55 9.9626 Tf -115.206 -11.9551 Td[(mld_n_ovr_)]TJ/F15 9.9626 Tf 95.6406 0 Td[(Num)28(b)-27(e)-1(r)-333(of)-333(o)28(v)28(erlap)1(s)]TJ/F55 9.9626 Tf -95.6406 -11.9552 Td[(mld_sub_restr_)]TJ/F15 9.9626 Tf 95.6406 0 Td[('HALO')1(,)-333('NONE')]TJ/F55 9.9626 Tf -95.6406 -11.9552 Td[(mld_sub_prol_)]TJ/F15 9.9626 Tf 95.6406 0 Td[('S)1(UM',)-333('NO)1(NE')]TJ/F55 9.9626 Tf -95.6406 -11.9551 Td[(mld_sub_solve_)]TJ/F15 9.9626 Tf 95.6406 0 Td[('ILU',)-333('M)1(ILU',)-333('ILUT',)-333('SLU')1(,)-334(')1(UMF')]TJ/F55 9.9626 Tf -95.6406 -11.9552 Td[(mld_sub_ren_)]TJ/F15 9.9626 Tf 95.6406 0 Td[(MANCANO)-333(LE)-333(S)1(T)-1(RINGHE)]TJ/F55 9.9626 Tf -95.6406 -11.9552 Td[(mld_sub_fill_in_)]TJ/F15 9.9626 Tf 95.6406 0 Td[(lev)28(e)-1(l)-333(of)-333(\014)1(ll-in)-333(in)-332(lo)-28(cal)-334(d)1(iagonal)-333(b)1(lo)-28(c)28(ks)-1(,)-333(when)-333(ILU-t)28(yp)-28(e)-333(factorization)1(s)-334(are)-334(u)1(s)-1(ed)]TJ
 ET
-1 0 0 1 500.3935 91.633 cm
+1 0 0 1 123.8606 389.2774 cm
+0 g 0 G
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+BT
+/F15 10.9091 Tf 123.8606 389.2774 Td[(T)83(ab)1(le)-334(5:)-444(P)28(aramete)-1(r)1(s)-334(for)-333(S)1(c)27(h)28(w)28(arz)-334(smo)-28(other/p)1(rec)-1(on)1(diti)1(oner)-333(t)27(y)1(p)-28(e.)]TJ
+ET
+1 0 0 1 429.1942 389.2774 cm
+0 g 0 G
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+0 g 0 G
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+BT
+/F15 10.9091 Tf 122.3998 362.7217 Td[(not)1(ing)-403(th)1(at,)-421(th)1(e)-404(class)-1(ical)-403(AS)-403(metho)-28(d)-402(c)-1(or)1(res)-1(p)-27(ond)1(s)-404(to)-403(th)1(e)-404(coupl)1(e)]TJ 0 -13.5492 Td[(of)-321(v)56(alues)-322('HALO')-321(and)-321('S)1(UM')-321(of)-321(the)-322(argu)1(m)-1(en)28(t)]TJ/F55 10.9091 Tf 220.4316 0 Td[(val)]TJ/F15 10.9091 Tf 17.1816 0 Td[(,)-324(f)1(or)-322(t)1(he)-322(v)56(alues)]TJ/F55 10.9091 Tf -237.6132 -13.5492 Td[(mld_sub_restr_)]TJ/F15 10.9091 Tf 84.1997 0 Td[(and)]TJ/F55 10.9091 Tf 21.5945 0 Td[(mld_sub_prol_)]TJ/F15 10.9091 Tf 78.4725 0 Td[(of)-368(th)1(e)-369(argu)1(m)-1(en)28(t)]TJ/F55 10.9091 Tf 81.1775 0 Td[(what)]TJ/F15 10.9091 Tf 22.9088 0 Td[(,)-377(re-)]TJ -288.353 -13.5492 Td[(sp)-28(ec)-1(ti)1(v)28(e)-1(ly)84(.)-459(W)1(hile,)-339(th)1(e)-339(RAS)-338(me)-1(th)1(o)-28(d)-338(corr)1(e)-1(sp)-28(on)1(ds)-338(to)-338(the)-338(c)-1(ou)1(ple)-338(of)]TJ 0 -13.5492 Td[(v)56(alues)-368(')1(NONE')-367(an)1(d)-367('S)1(UM')-367(an)1(d)-367(AS)1(H)-367(m)-1(etho)-27(d)-367(c)-1(or)1(res)-1(p)-27(ond)1(s)-368(to)-367(th)1(e)]TJ 0 -13.5492 Td[(coupl)1(e)-334(of)-333(v)56(alues)-334('HALO)1(')-333(and)-333('NO)1(NE'.)]TJ/F19 11.9552 Tf 0 -30.4849 Td[(6.)-1(2)-1125(Pre)-1(condi)-1(ti)-1(one)-1(r)-375(Appli)-1(ca)1(t)-1(io)-1(n)]TJ/F15 10.9091 Tf 0 -21.0272 Td[(On)1(c)-1(e)-277(t)1(he)-277(p)1(rec)-1(on)1(diti)1(oner)-276(has)-277(b)-27(e)-1(en)-276(bu)1(ilt,)-287(it)-276(ma)27(y)-276(b)-27(e)-277(ap)1(plied)-276(at)-276(e)-1(ac)28(h)]TJ 0 -13.5492 Td[(iterati)1(on)-339(of)-339(a)-339(K)1(rylo)28(v)-339(solv)28(er)-339(b)28(y)-339(calli)1(ng)-339(th)1(e)-340(rou)1(tin)1(e)]TJ/F55 10.9091 Tf 239.5287 0 Td[(mld_precaply)]TJ/F15 10.9091 Tf -239.5287 -13.5492 Td[(\050CAMBIARE)-222(NOM)1(E)-222(R)28(OUTI)-1(NE)-221(NEL)-222(S)1(OFTW)111(ARE)-222(E)1(VIT)83(ANDO)]TJ 0 -13.5492 Td[(L'UNDE)1(RSCORE\051)1(,)-377(whose)-378(AP)1(I)-377(is)-377(s)-1(h)1(o)28(w)-1(n)-376(in)-376(Figu)1(re)]TJ
+ET
+1 0 0 1 371.0883 202.816 cm
+0 0 1 rg 0 0 1 RG
+1 0 0 1 -371.0883 -202.816 cm
+BT
+/F15 10.9091 Tf 371.0883 202.816 Td[(5)]TJ
+ET
+1 0 0 1 376.5428 202.816 cm
+0 g 0 G
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+%!PS-AdobeFont-1.1: CMBX10 1.00B
+%%CreationDate: 1992 Feb 19 19:54:06
+% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
+11 dict begin
+/FontInfo 7 dict dup begin
+/version (1.00B) readonly def
+/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
+/FullName (CMBX10) readonly def
+/FamilyName (Computer Modern) readonly def
+/Weight (Bold) readonly def
+/ItalicAngle 0 def
+/isFixedPitch false def
+end readonly def
+/FontName /BXVSRE+CMBX10 def
+/PaintType 0 def
+/FontType 1 def
+/FontMatrix [0.001 0 0 0.001 0 0] readonly def
+/Encoding 256 array
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+dup 12 /fi put
+dup 39 /quoteright put
+dup 40 /parenleft put
+dup 41 /parenright put
+dup 44 /comma put
+dup 45 /hyphen put
+dup 46 /period put
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 dup 49 /one put
 dup 50 /two put
 dup 51 /three put
 dup 52 /four put
 dup 53 /five put
+dup 54 /six put
+dup 55 /seven put
+dup 56 /eight put
 dup 57 /nine put
 dup 58 /colon put
+dup 59 /semicolon put
+dup 63 /question put
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 dup 66 /B put
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 dup 69 /E put
 dup 70 /F put
 dup 71 /G put
+dup 72 /H put
 dup 73 /I put
-dup 75 /K put
 dup 76 /L put
 dup 77 /M put
 dup 78 /N put
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 dup 84 /T put
 dup 85 /U put
 dup 86 /V put
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 dup 97 /a put
 dup 98 /b put
 dup 99 /c put
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 dup 104 /h put
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 dup 108 /l put
 dup 109 /m put
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 dup 117 /u put
 dup 118 /v put
 dup 119 /w put
-dup 120 /x put
 dup 121 /y put
 dup 122 /z put
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+/BaseFont /BXVSRE+CMBX10
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 >> endobj
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 /Ascent 694
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-/FontName /TAPIAO+CMTI10
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+/FontDescriptor 85 0 R
 >> endobj
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-%%CreationDate: 1992 Feb 19 19:54:06
+%!PS-AdobeFont-1.1: CMR12 1.0
+%%CreationDate: 1991 Aug 20 16:38:05
 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
 11 dict begin
 /FontInfo 7 dict dup begin
-/version (1.00B) readonly def
+/version (1.0) readonly def
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-/FullName (CMBX10) readonly def
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+/Weight (Medium) readonly def
 /ItalicAngle 0 def
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 /FontType 1 def
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-dup 39 /quoteright put
-dup 40 /parenleft put
-dup 41 /parenright put
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 dup 44 /comma put
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-dup 68 /D put
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