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mld2p4-2:

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Docs updates
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Salvatore Filippone
2016-02-29 14:15:38 +00:00
parent 9c35e30fea
commit 1201cdfad8
137 changed files with 10543 additions and 1524 deletions
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docs/html/node13.html
+9 -11
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@@ -1,6 +1,6 @@
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 3.2 Final//EN">
<!--Converted with LaTeX2HTML 2008 (1.71)
<!--Converted with LaTeX2HTML 2012 (1.2)
original version by: Nikos Drakos, CBLU, University of Leeds
* revised and updated by: Marcus Hennecke, Ross Moore, Herb Swan
* with significant contributions from:
@@ -13,7 +13,7 @@ original version by: Nikos Drakos, CBLU, University of Leeds
<META NAME="resource-type" CONTENT="document">
<META NAME="distribution" CONTENT="global">
<META NAME="Generator" CONTENT="LaTeX2HTML v2008">
<META NAME="Generator" CONTENT="LaTeX2HTML v2012">
<META HTTP-EQUIV="Content-Style-Type" CONTENT="text/css">
<LINK REL="STYLESHEET" HREF="userhtml.css">
@@ -72,7 +72,7 @@ The basic idea of this algorithm is to build a coarse set of vertices
WIDTH="32" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
SRC="img45.png"
ALT="$W_C$"> by suitably grouping the vertices of <IMG
WIDTH="23" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
WIDTH="23" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
SRC="img11.png"
ALT="$W$"> into disjoint subsets
(aggregates), and to define the coarse-to-fine space transfer operator <IMG
@@ -87,7 +87,7 @@ Three main steps can be identified in the smoothed aggregation procedure:
<OL>
<LI>coarsening of the vertex set <IMG
WIDTH="23" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
WIDTH="23" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
SRC="img11.png"
ALT="$W$">, to obtain <IMG
WIDTH="32" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
@@ -111,7 +111,6 @@ Three main steps can be identified in the smoothed aggregation procedure:
ALT="$A_C$">.
</LI>
</OL>
<P>
To perform the coarsening step, we have implemented the aggregation algorithm sketched
in [<A
@@ -122,7 +121,7 @@ in which each aggregate <IMG
WIDTH="26" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
SRC="img71.png"
ALT="$N_r$"> is made of vertices of <IMG
WIDTH="23" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
WIDTH="23" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
SRC="img11.png"
ALT="$W$"> that are <I>strongly coupled</I>
to a certain root vertex <IMG
@@ -138,7 +137,7 @@ N_r = \left\{s \in W: |a_{rs}| > \theta \sqrt{|a_{rr}a_{ss}|} \right\}
-->
<IMG
WIDTH="319" HEIGHT="38" BORDER="0"
WIDTH="320" HEIGHT="38" BORDER="0"
SRC="img73.png"
ALT="\begin{displaymath}N_r = \left\{s \in W: \vert a_{rs}\vert &gt; \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="100%" ALIGN="CENTER">
<TR VALIGN="MIDDLE"><TD ALIGN="CENTER" NOWRAP><A NAME="eq:tent_prol"></A><IMG
WIDTH="290" HEIGHT="52" BORDER="0"
WIDTH="291" HEIGHT="52" BORDER="0"
SRC="img79.png"
ALT="\begin{displaymath}
P=(p_{ij}), \quad p_{ij}=
@@ -255,7 +254,7 @@ Schwarz method [<A
HREF="node25.html#BREZINA_VANEK">1</A>,<A
HREF="node25.html#StubenGMD69_99">24</A>].
A simple choice for <IMG
WIDTH="16" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
WIDTH="16" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
SRC="img84.png"
ALT="$S$"> is the damped Jacobi smoother:
<BR>
@@ -268,7 +267,7 @@ S = I - \omega D^{-1} A ,
-->
<TABLE WIDTH="100%" ALIGN="CENTER">
<TR VALIGN="MIDDLE"><TD ALIGN="CENTER" NOWRAP><A NAME="eq:jac_smoother"></A><IMG
WIDTH="126" HEIGHT="30" BORDER="0"
WIDTH="125" HEIGHT="30" BORDER="0"
SRC="img85.png"
ALT="\begin{displaymath}
S = I - \omega D^{-1} A ,
@@ -286,7 +285,6 @@ using some estimate of the spectral radius of <IMG
SRC="img87.png"
ALT="$D^{-1}A$"> [<A
HREF="node25.html#BREZINA_VANEK">1</A>].
<P>
<HR>
<!--Navigation Panel-->