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Further docs fixes.
This commit is contained in:
Salvatore Filippone
2008-07-23 09:08:06 +00:00
parent cf4061d09e
commit 5a8ed47797
34 changed files with 5454 additions and 5187 deletions
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@@ -27,30 +27,30 @@ original version by: Nikos Drakos, CBLU, University of Leeds
<BODY >
<DIV CLASS="navigation"><!--Navigation Panel-->
<A NAME="tex2html200"
<A NAME="tex2html194"
HREF="node12.html">
<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next"
SRC="file:/usr/share/latex2html/icons/next.png"></A>
<A NAME="tex2html196"
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HREF="node10.html">
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SRC="file:/usr/share/latex2html/icons/up.png"></A>
<A NAME="tex2html190"
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<BR>
<B> Next:</B> <A NAME="tex2html201"
<B> Next:</B> <A NAME="tex2html195"
HREF="node12.html">Smoothed Aggregation</A>
<B> Up:</B> <A NAME="tex2html197"
<B> Up:</B> <A NAME="tex2html191"
HREF="node10.html">Multi-level Domain Decomposition Background</A>
<B> Previous:</B> <A NAME="tex2html191"
<B> Previous:</B> <A NAME="tex2html185"
HREF="node10.html">Multi-level Domain Decomposition Background</A>
&nbsp; <B> <A NAME="tex2html199"
&nbsp; <B> <A NAME="tex2html193"
HREF="node2.html">Contents</A></B>
<BR>
<BR></DIV>
@@ -300,15 +300,15 @@ ILU(<SPAN CLASS="MATH"><IMG
WIDTH="27" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
SRC="img35.png"
ALT="$p,t$"></SPAN>) [<A
HREF="node30.html#Saad_book">19</A>, Chapter 10].
HREF="node24.html#Saad_book">19</A>, Chapter 10].
<P>
A variant of the classical AS preconditioner that outperforms it
in terms of convergence rate and of computation and communication
time on parallel distributed-memory computers is the so-called <SPAN CLASS="textit">Restricted AS
(RAS)</SPAN> preconditioner&nbsp;[<A
HREF="node30.html#CAI_SARKIS">5</A>,<A
HREF="node30.html#EFSTATHIOU">13</A>]. It
HREF="node24.html#CAI_SARKIS">5</A>,<A
HREF="node24.html#EFSTATHIOU">13</A>]. It
is obtained by zeroing the components of <SPAN CLASS="MATH"><IMG
WIDTH="23" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
SRC="img32.png"
@@ -391,8 +391,8 @@ of <SPAN CLASS="MATH"><IMG
WIDTH="24" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
SRC="img10.png"
ALT="$W$"></SPAN> increases [<A
HREF="node30.html#dd1_94">7</A>,<A
HREF="node30.html#dd2_96">20</A>]. To reduce the dependency
HREF="node24.html#dd1_94">7</A>,<A
HREF="node24.html#dd2_96">20</A>]. 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 <SPAN CLASS="MATH"><IMG
@@ -647,12 +647,12 @@ in which the coarse-level correction is re-applied starting from the current
coarse-level system. The corresponding preconditioners, called <SPAN CLASS="textit">multi-level</SPAN>
preconditioners, can significantly reduce the computational cost of preconditioning
with respect to the two-level case (see [<A
HREF="node30.html#dd2_96">20</A>, Chapter 3]).
HREF="node24.html#dd2_96">20</A>, Chapter 3]).
Additive and hybrid multilevel preconditioners
are obtained as direct extensions of the two-level counterparts.
For a detailed descrition of them, the reader is
referred to [<A
HREF="node30.html#dd2_96">20</A>, Chapter 3].
HREF="node24.html#dd2_96">20</A>, Chapter 3].
The algorithm for the application of a multi-level hybrid
post-smoothed preconditioner <SPAN CLASS="MATH"><IMG
WIDTH="23" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
@@ -741,30 +741,30 @@ $w = y_1$;
<DIV CLASS="navigation"><HR>
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<BR>
<B> Next:</B> <A NAME="tex2html201"
<B> Next:</B> <A NAME="tex2html195"
HREF="node12.html">Smoothed Aggregation</A>
<B> Up:</B> <A NAME="tex2html197"
<B> Up:</B> <A NAME="tex2html191"
HREF="node10.html">Multi-level Domain Decomposition Background</A>
<B> Previous:</B> <A NAME="tex2html191"
<B> Previous:</B> <A NAME="tex2html185"
HREF="node10.html">Multi-level Domain Decomposition Background</A>
&nbsp; <B> <A NAME="tex2html199"
&nbsp; <B> <A NAME="tex2html193"
HREF="node2.html">Contents</A></B> </DIV>
<!--End of Navigation Panel-->
<ADDRESS>