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Added description for the psb_krylov driver routine.

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Alfredo Buttari
2006-07-07 16:03:38 +00:00
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docs/pdf/methods.tex
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@@ -4,6 +4,95 @@
In this chapter we provide routines for preconditioners and iterative
methods.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% Krylov Methods driver routine
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subroutine{psb\_krylov \label{cg}}{Krylov Methods Driver Routine}
This subroutine is a driver that provides a general interface for all
the Krylov-Subspace family methods implemented in PSBLAS-2.0. The
stopping criterion is the normwise backward error, in the infinity
norm, i.e. the iteration is stopped when
\[ \frac{\|r\|}{(\|A\|\|x\|+\|b\|)} < eps \]
or
\[ \frac{\|r_i\|}{\|b\|_2} < eps \]
according to the value passed through the istop argument (see later).
\syntax{call psb\_krylov}{method,a,prec,b,x,eps,desc\_a,info,itmax,iter,err,itrace,istop}
\begin{description}
\item[\bf On Entry]
\item[method] a string that defines the iterative method to be
used. Valid values in PSBLAS-2.0 are:
\begin{description}
\item[CG]: the Conjugate gradient method;
\item[CGS]:the Conjugate Gradient Stabilized method;
\item[BICG]: the Bi-Conjugate Gradient method;
\item[BICGSTAB]: the Bi-Conjugate Gradient Stabilized method;
\item[BICGSTABL]: the Bi-Conjugate Gradient Stabilized method with restarting;
\item[RGMRES]: the Generalized Minimal Residual method with restarting.
\end{description}
\item[a] the local portion of global sparse matrix
$A$. \\
Scope: {\bf local} \\
Type: {\bf required}\\
Specified as: a structured data of type \spdata.
\item[prec] The data structure containing the preconditioner.\\
Scope: {\bf local} \\
Type: {\bf required}\\
Specified as: a structured data of type \precdata.
\item[b] The RHS vector. \\
Scope: {\bf local} \\
Type: {\bf required}\\
Specified as: a rank one array.
\item[x] The initial guess. \\
Scope: {\bf local} \\
Type: {\bf required}\\
Specified as: a rank one array.
\item[eps] The stopping tolerance. \\
Scope: {\bf global} \\
Type: {\bf required}\\
Specified as: a real number.
\item[desc\_a] contains data structures for communications.\\
Scope: {\bf local} \\
Type: {\bf required}\\
Specified as: a structured data of type \descdata.
\item[itmax] The maximum number of iterations to perform.\\
Scope: {\bf global} \\
Type: {\bf optional}\\
Default: $itmax = 1000$.\\
Specified as: an integer variable $itmax \ge 1$.
\item[itrace] If $>0$ print out an informational message about
convergence every $itrace$ iterations.\\
Scope: {\bf global} \\
Type: {\bf optional}\\
\item[istop] An integer specifying the stopping criterion.\\
Scope: {\bf global} \\
Type: {\bf optional}\\
\item[\bf On Return]
\item[x] The computed solution. \\
Scope: {\bf local} \\
Type: {\bf required}\\
Specified as: a rank one array.
\item[iter] The number of iterations performed.\\
Scope: {\bf global} \\
Type: {\bf optional}\\
Returned as: an integer variable.
\item[err] The error estimate on exit.\\
Scope: {\bf global} \\
Type: {\bf optional}\\
Returned as: a real number.
\item[info] An error code.\\
Scope: {\bf global} \\
Type: {\bf optional}\\
Returned as: an integer variable.
\end{description}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%