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We note that for $\delta=0$ the three variants of the AS preconditioner are all equal to the block-Jacobi preconditioner. @@ -383,7 +383,7 @@ preconditioned iterative solvers deteriorates as the number $m$ of partitions of $W$ increases [7, \begin{displaymath} M_{C}^{-1}= R_C^T A_C^{-1} R_C, @@ -566,7 +566,7 @@ M_{2LH-PRE}^{-1} = M_{C}^{-1} + \left( I - M_{C}^{-1}A \right) M_{1L}^{-1}. --> <IMG - WIDTH=, is reported, for example, in Figure 1. Here the number of levels is denoted by $nlev$ and the levels are numbered in increasing order starting from the finest one, i.e. the finest level is level 1; the coarse matrix and the corresponding basic preconditioner at each level $l$ are denoted by $\framebox{ \begin{minipage}{.85\textwidth} {\small \begin{tabbing} -\quad \=\quad \=\quad \=\quad \\[-1mm] -$v_1 = v$; \\[2mm] +\quad \=\quad \=\quad \=\quad \\[-1mm]$v_1 = v$; \\[2mm] \textbf{for $l=2, nlev$\ do}\\[1mm] \> ! transfer $v_{l-1}$\ to the next coarser level\\ \> $v_l = R_lv_{l-1}$\ \\[1mm] @@ -727,7 +726,7 @@ $w = y_1$; \begin{tabbing} \quad \=\quad... ...= y_l+r_l$\\ -\textbf{endfor} \\ [1mm] +\textbf{endfor} \ [1mm] $w = y_1$; \end{tabbing}} \end{minipage}}"> diff --git a/docs/html/node13.html b/docs/html/node13.html index b4bd7eae..856d6b39 100644 --- a/docs/html/node13.html +++ b/docs/html/node13.html @@ -1,6 +1,6 @@ - \begin{displaymath}N_r = \left\{s \in W: \vert a_{rs}\vert > \theta \sqrt{\vert a_{rr}a_{ss}\vert} \right\} \cup \left\{ r \right\} , @@ -202,7 +201,7 @@ P=(p_{ij}), \quad p_{ij}= --> <TABLE WIDTH= \begin{displaymath} P=(p_{ij}), \quad p_{ij}= @@ -255,7 +254,7 @@ Schwarz method [<A HREF=1,24]. A simple choice for $S$ is the damped Jacobi smoother:
@@ -268,7 +267,7 @@ S = I - \omega D^{-1} A , -->
\begin{displaymath} S = I - \omega D^{-1} A , @@ -286,7 +285,6 @@ using some estimate of the spectral radius of <IMG SRC= [1]. -

diff --git a/docs/html/node14.html b/docs/html/node14.html index 87a6502d..3b579598 100644 --- a/docs/html/node14.html +++ b/docs/html/node14.html @@ -1,6 +1,6 @@ -

- + + +


diff --git a/docs/html/node20.html b/docs/html/node20.html index 646cdd9b..2b24d179 100644 --- a/docs/html/node20.html +++ b/docs/html/node20.html @@ -1,6 +1,6 @@ -
\begin{displaymath} Ax=b, @@ -84,8 +84,7 @@ where <IMG WIDTH= is a square, real or complex, sparse matrix with a symmetric -sparsity pattern. -These preconditioners have the following general features: +sparsity pattern. These preconditioners have the following general features: