mld2p4:
configure.ac configure docs/html docs/html/WARNINGS docs/html/images.aux docs/html/images.log docs/html/images.out docs/html/images.pl docs/html/images.tex docs/html/img1.png docs/html/img10.png docs/html/img100.png docs/html/img11.png docs/html/img12.png docs/html/img13.png docs/html/img14.png docs/html/img15.png docs/html/img16.png docs/html/img17.png docs/html/img18.png docs/html/img19.png docs/html/img2.png docs/html/img20.png docs/html/img21.png docs/html/img22.png docs/html/img23.png docs/html/img24.png docs/html/img25.png docs/html/img26.png docs/html/img27.png docs/html/img28.png docs/html/img29.png docs/html/img3.png docs/html/img30.png docs/html/img31.png docs/html/img32.png docs/html/img33.png docs/html/img34.png docs/html/img35.png docs/html/img36.png docs/html/img37.png docs/html/img38.png docs/html/img39.png docs/html/img4.png docs/html/img40.png docs/html/img41.png docs/html/img42.png docs/html/img43.png docs/html/img44.png docs/html/img45.png docs/html/img46.png docs/html/img47.png docs/html/img48.png docs/html/img49.png docs/html/img5.png docs/html/img50.png docs/html/img51.png docs/html/img52.png docs/html/img53.png docs/html/img54.png docs/html/img55.png docs/html/img56.png docs/html/img57.png docs/html/img58.png docs/html/img59.png docs/html/img6.png docs/html/img60.png docs/html/img61.png docs/html/img62.png docs/html/img63.png docs/html/img64.png docs/html/img65.png docs/html/img66.png docs/html/img67.png docs/html/img68.png docs/html/img69.png docs/html/img7.png docs/html/img70.png docs/html/img71.png docs/html/img72.png docs/html/img73.png docs/html/img74.png docs/html/img75.png docs/html/img76.png docs/html/img77.png docs/html/img78.png docs/html/img79.png docs/html/img8.png docs/html/img80.png docs/html/img81.png docs/html/img82.png docs/html/img83.png docs/html/img84.png docs/html/img85.png docs/html/img86.png docs/html/img87.png docs/html/img88.png docs/html/img89.png docs/html/img9.png docs/html/img90.png docs/html/img91.png docs/html/img92.png docs/html/img93.png docs/html/img94.png docs/html/img95.png docs/html/img96.png docs/html/img97.png docs/html/img98.png docs/html/img99.png docs/html/index.html docs/html/internals.pl docs/html/labels.pl docs/html/node1.html docs/html/node10.html docs/html/node11.html docs/html/node12.html docs/html/node13.html docs/html/node14.html docs/html/node15.html docs/html/node16.html docs/html/node17.html docs/html/node18.html docs/html/node19.html docs/html/node2.html docs/html/node20.html docs/html/node21.html docs/html/node22.html docs/html/node23.html docs/html/node24.html docs/html/node25.html docs/html/node26.html docs/html/node27.html docs/html/node28.html docs/html/node29.html docs/html/node3.html docs/html/node30.html docs/html/node31.html docs/html/node4.html docs/html/node5.html docs/html/node6.html docs/html/node7.html docs/html/node8.html docs/html/node9.html docs/html/userhtml.css docs/html/userhtml.html docs/pdf/building.tex docs/userguide.pdf examples/fileread/mld_cexample_1lev.f90 examples/fileread/mld_cexample_ml.f90 examples/fileread/mld_dexample_1lev.f90 examples/fileread/mld_dexample_ml.f90 examples/fileread/mld_sexample_1lev.f90 examples/fileread/mld_sexample_ml.f90 examples/fileread/mld_zexample_1lev.f90 examples/fileread/mld_zexample_ml.f90 mlprec/mld_cprecset.f90 mlprec/mld_dprecset.f90 mlprec/mld_sprecset.f90 mlprec/mld_zprecset.f90 test/fileread/cf_sample.f90 test/fileread/df_sample.f90 test/fileread/runs/cfs.inp test/fileread/runs/dfs.inp test/fileread/runs/sfs.inp test/fileread/runs/zfs.inp test/fileread/sf_sample.f90 test/fileread/zf_sample.f90 Fixed I/O for fileread samples. Fixed precset typo. Updated documentation for building. Included HTML pages.stopcriterion
Salvatore Filippone
17 years ago
parent
a2b52fd606
commit
b7445f740c
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No implementation found for style `pstricks'
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No implementation found for style `fancybox'
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No implementation found for style `ifpdf'
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No implementation found for style `hyperref'
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No implementation found for style `ifthen'
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No implementation found for style `graphicx'
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No implementation found for style `rotating'
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redefining command \thepage
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The userhtml.aux file was not found, so sections will not be numbered
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and cross-references will be shown as icons.
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? brace missing for \setlength
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No number for "Applicationofthemulti-levelhybridpost-smoothedpreconditioner."
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No number for "Preconditionertypes,correspondingstringsanddefaultchoices."
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No number for "Setupandapplicationofthedefaultmulti-levelSchwarzpreconditioner."
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No number for "Setupofahybridthree-levelSchwarzpreconditioner."
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No number for "Setupofanadditivethree-levelSchwarzpreconditioner."
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No number for "Setupofaone-levelSchwarzpreconditioner."
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No number for "Parametersdefiningthetypeofmulti-levelpreconditioner."
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No number for "Parametersdefiningtheone-levelpreconditionerusedassmoother."
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No number for "Parametersdefiningtheaggregationalgorithm."
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No number for "Parametersdefiningthecoarse-spacecorrectionatthecoarsestlevel."
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couldn't convert character ecaron into available encodings
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...set $ACCENT_IMAGES to get an image
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\relax
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\ifx\hyper@anchor\@undefined
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\global \let \oldcontentsline\contentsline
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\gdef \contentsline#1#2#3#4{\oldcontentsline{#1}{#2}{#3}}
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\global \let \oldnewlabel\newlabel
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\gdef \newlabel#1#2{\newlabelxx{#1}#2}
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\gdef \newlabelxx#1#2#3#4#5#6{\oldnewlabel{#1}{{#2}{#3}}}
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\AtEndDocument{\let \contentsline\oldcontentsline
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\let \newlabel\oldnewlabel}
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\else
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\global \let \hyper@last\relax
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\fi
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\providecommand*\HyPL@Entry[1]{}
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\HyPL@Entry{0 << /S /D >> }
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This is pdfTeXk, Version 3.141592-1.40.3 (Web2C 7.5.6) (format=latex 2008.5.20) 22 JUL 2008 18:30
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entering extended mode
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%&-line parsing enabled.
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**./images.tex
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(./images.tex
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LaTeX2e <2005/12/01>
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Babel <v3.8h> and hyphenation patterns for english, usenglishmax, dumylang, noh
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yphenation, arabic, basque, bulgarian, coptic, welsh, czech, slovak, german, ng
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erman, danish, esperanto, spanish, catalan, galician, estonian, farsi, finnish,
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french, greek, monogreek, ancientgreek, croatian, hungarian, interlingua, ibyc
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us, indonesian, icelandic, italian, latin, mongolian, dutch, norsk, polish, por
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tuguese, pinyin, romanian, russian, slovenian, uppersorbian, serbian, swedish,
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turkish, ukenglish, ukrainian, loaded.
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(/usr/share/texmf/tex/latex/base/article.cls
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Document Class: article 2005/09/16 v1.4f Standard LaTeX document class
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(/usr/share/texmf/tex/latex/base/size11.clo
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File: size11.clo 2005/09/16 v1.4f Standard LaTeX file (size option)
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)
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\c@part=\count79
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\c@subparagraph=\count84
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\c@table=\count86
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\abovecaptionskip=\skip41
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\belowcaptionskip=\skip42
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\bibindent=\dimen102
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) (/usr/share/texmf/tex/latex/pstricks/pstricks.sty
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Package: pstricks 2006/08/10 v0.32 LaTeX wrapper for `PSTricks' (RN,HV)
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(/usr/share/texmf/tex/generic/pstricks/pstricks.tex
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`PSTricks' v1.15 <2006/12/22> (tvz)
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\pst@dima=\dimen103
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\pst@dimd=\dimen106
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\pst@dimh=\dimen108
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\pst@hbox=\box26
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\pst@boxg=\box27
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\pst@cnta=\count87
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\pst@cntc=\count89
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\pst@cntd=\count90
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\pst@cntg=\count91
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\pst@cnth=\count92
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\pst@toks=\toks14
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(/usr/share/texmf/tex/generic/pstricks/pstricks.con)
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\psunit=\dimen109
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\psxunit=\dimen110
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\everypsbox=\toks16
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\pslabelsep=\dimen115
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\psk@shift=\dimen116
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\pst@shift=\dimen117
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\theoverlaybox=\box28
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)
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File: pstricks.tex 2006/12/22 v1.15 `PSTricks' (tvz)
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(/usr/share/texmf/tex/latex/xcolor/xcolor.sty
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Package: xcolor 2007/01/21 v2.11 LaTeX color extensions (UK)
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(/usr/share/texmf/tex/latex/config/color.cfg
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File: color.cfg 2007/01/18 v1.5 color configuration of teTeX/TeXLive
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)
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Package xcolor Info: Package option `override' ignored on input line 216.
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Package xcolor Info: Driver file: dvips.def on input line 225.
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File: dvips.def 1999/02/16 v3.0i Driver-dependant file (DPC,SPQR)
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)
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Package xcolor Info: Model `cmy' substituted by `cmy0' on input line 1337.
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Package xcolor Info: Model `RGB' extended on input line 1353.
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Package xcolor Info: Model `HTML' substituted by `rgb' on input line 1355.
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Package xcolor Info: Model `tHsb' substituted by `hsb' on input line 1357.
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)) (/usr/share/texmf/tex/latex/fancybox/fancybox.sty
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Package: fancybox 2000/09/19 1.3
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Style option: `fancybox' v1.3 <2000/09/19> (tvz)
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\@fancybox=\box29
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\shadowsize=\dimen118
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\@Sbox=\box30
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\do@VerbBox=\toks17
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\the@fancyput=\toks18
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\this@fancyput=\toks19
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\EndVerbatimTokens=\toks20
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\Verbatim@Outfile=\write3
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\Verbatim@Infile=\read1
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) (/usr/share/texmf/tex/latex/amsfonts/amsfonts.sty
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Package: amsfonts 2001/10/25 v2.2f
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\@emptytoks=\toks21
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\symAMSa=\mathgroup4
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LaTeX Font Info: Overwriting math alphabet `\mathfrak' in version `bold'
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(Font) U/euf/m/n --> U/euf/b/n on input line 132.
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) (/usr/share/texmf/tex/generic/oberdiek/ifpdf.sty
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Package: ifpdf 2006/02/20 v1.4 Provides the ifpdf switch (HO)
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Package ifpdf Info: pdfTeX in pdf mode not detected.
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) (/usr/share/texmf/tex/latex/hyperref/hyperref.sty
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Package: hyperref 2007/02/07 v6.75r Hypertext links for LaTeX
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(/usr/share/texmf/tex/latex/graphics/keyval.sty
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Package: keyval 1999/03/16 v1.13 key=value parser (DPC)
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\KV@toks@=\toks22
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)
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\@linkdim=\dimen119
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\Hy@linkcounter=\count93
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\Hy@pagecounter=\count94
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File: pd1enc.def 2007/02/07 v6.75r Hyperref: PDFDocEncoding definition (HO)
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) (/usr/share/texmf/tex/latex/config/hyperref.cfg
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File: hyperref.cfg 2002/06/06 v1.2 hyperref configuration of TeXLive
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) (/usr/share/texmf/tex/latex/oberdiek/kvoptions.sty
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Package: kvoptions 2006/08/22 v2.4 Connects package keyval with LaTeX options (
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HO)
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)
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Package hyperref Info: Option `bookmarks' set `true' on input line 2238.
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Package hyperref Info: Option `bookmarksnumbered' set `true' on input line 2238
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.
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Package hyperref Info: Option `bookmarksopen' set `false' on input line 2238.
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Package hyperref Info: Option `plainpages' set `false' on input line 2238.
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Package hyperref Info: Option `pdfpagelabels' set `true' on input line 2238.
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Package hyperref Info: Option `colorlinks' set `true' on input line 2238.
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Package hyperref Info: Hyper figures OFF on input line 2288.
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Package hyperref Info: Link nesting OFF on input line 2293.
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Package hyperref Info: Hyper index ON on input line 2296.
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Package hyperref Info: Plain pages OFF on input line 2303.
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Package hyperref Info: Backreferencing OFF on input line 2308.
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Implicit mode ON; LaTeX internals redefined
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Package hyperref Info: Bookmarks ON on input line 2444.
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(/usr/share/texmf/tex/latex/html/url.sty
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Package: url 1999/03/02 ver 1.4 Verb mode for urls, email addresses, and file
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names
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)
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LaTeX Info: Redefining \url on input line 2599.
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\Fld@menulength=\count95
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Package hyperref Info: Hyper figures OFF on input line 3102.
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Package hyperref Info: Hyper index ON on input line 3110.
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Package hyperref Info: backreferencing OFF on input line 3117.
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Package hyperref Info: Link coloring ON on input line 3120.
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\Hy@abspage=\count96
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)
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*hyperref using default driver hdvips*
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(/usr/share/texmf/tex/latex/hyperref/hdvips.def
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File: hdvips.def 2007/02/07 v6.75r Hyperref driver for dvips
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File: pdfmark.def 2007/02/07 v6.75r Hyperref definitions for pdfmark specials
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Package: graphicx 1999/02/16 v1.0f Enhanced LaTeX Graphics (DPC,SPQR)
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Package: graphics 2006/02/20 v1.0o Standard LaTeX Graphics (DPC,SPQR)
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)
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Package: pstcol 2005/11/16 v1.2 LaTeX wrapper for `PSTricks' (RN,HV)
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Package pstcol Warning: ************************************
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(pstcol) The package `pstcol' is obsolet!
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(pstcol) You should use `pstricks' directly:
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(pstcol) \usepackage{pstricks}
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(pstcol) ************************************.
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! LaTeX Error: Option clash for package pstricks.
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See the LaTeX manual or LaTeX Companion for explanation.
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Type H <return> for immediate help.
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...
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l.21
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The package pstricks has already been loaded with options:
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[]
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There has now been an attempt to load it with options
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[noxcolor]
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Adding the global options:
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,noxcolor
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to your \documentclass declaration may fix this.
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Try typing <return> to proceed.
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Package: inputenc 2006/05/05 v1.1b Input encoding file
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\openout5 = `images.out'.
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Package hyperref Warning: Rerun to get /PageLabels entry.
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Here is how much of TeX's memory you used:
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4265 strings out of 94074
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55276 string characters out of 1167173
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134209 words of memory out of 1500000
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7519 multiletter control sequences out of 10000+50000
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10304 words of font info for 41 fonts, out of 1200000 for 2000
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645 hyphenation exceptions out of 8191
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30i,8n,37p,306b,390s stack positions out of 5000i,500n,6000p,200000b,10000s
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Output written on images.dvi (100 pages, 72052 bytes).
|
||||
@ -0,0 +1,657 @@
|
||||
# LaTeX2HTML 2002-2-1 (1.71)
|
||||
# Associate images original text with physical files.
|
||||
|
||||
|
||||
$key = q/w=M^{-1}v;MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="87" HEIGHT="21" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="|."$dir".q|img60.png"
|
||||
ALT="$w=M^{-1}v$">|;
|
||||
|
||||
$key = q/w;MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="17" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="|."$dir".q|img87.png"
|
||||
ALT="$w$">|;
|
||||
|
||||
$key = q/W_i^{delta};MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="31" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="|."$dir".q|img26.png"
|
||||
ALT="$W_i^{\delta}$">|;
|
||||
|
||||
$key = q/{displaymath}M_{2LA}^{-1}=M_{C}^{-1}+M_{1L}^{-1}.{displaymath};MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="165" HEIGHT="32" BORDER="0"
|
||||
SRC="|."$dir".q|img52.png"
|
||||
ALT="\begin{displaymath}
|
||||
M_{2LA}^{-1} = M_{C}^{-1} + M_{1L}^{-1}.
|
||||
\end{displaymath}">|;
|
||||
|
||||
$key = q/M_{1L}^{-1};MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="42" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="|."$dir".q|img54.png"
|
||||
ALT="$M_{1L}^{-1}$">|;
|
||||
|
||||
$key = q/M_l;MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="27" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="|."$dir".q|img64.png"
|
||||
ALT="$M_l$">|;
|
||||
|
||||
$key = q/W;MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="24" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="|."$dir".q|img10.png"
|
||||
ALT="$W$">|;
|
||||
|
||||
$key = q/W_i^0subsetW;MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="73" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="|."$dir".q|img12.png"
|
||||
ALT="$W_i^0 \subset W$">|;
|
||||
|
||||
$key = q/E={(i,j):a_{ij}neq0};MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="162" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="|."$dir".q|img6.png"
|
||||
ALT="$E=\{(i,j) : a_{ij} \neq 0\}$">|;
|
||||
|
||||
$key = q/nlev;MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="37" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="|."$dir".q|img61.png"
|
||||
ALT="$nlev$">|;
|
||||
|
||||
$key = q/A_i^deltaw_i=v_i;MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="80" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="|."$dir".q|img31.png"
|
||||
ALT="$A_i^\delta w_i = v_i$">|;
|
||||
|
||||
$key = q/M_{1L};MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="38" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="|."$dir".q|img48.png"
|
||||
ALT="$M_{1L}$">|;
|
||||
|
||||
$key = q/R_i^delta;MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="25" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="|."$dir".q|img38.png"
|
||||
ALT="$R_i^\delta$">|;
|
||||
|
||||
$key = q/op(M^{-1})=M^{-T};MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="135" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="|."$dir".q|img98.png"
|
||||
ALT="$op(M^{-1}) = M^{-T}$">|;
|
||||
|
||||
$key = q/W_i^{delta-1};MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="48" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="|."$dir".q|img15.png"
|
||||
ALT="$W_i^{\delta-1}$">|;
|
||||
|
||||
$key = q/cup_{i=1}^mW_i^0=W;MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="107" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="|."$dir".q|img13.png"
|
||||
ALT="$\cup_{i=1}^m W_i^0 = W$">|;
|
||||
|
||||
$key = q/delta=0;MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="45" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="|."$dir".q|img42.png"
|
||||
ALT="$\delta=0$">|;
|
||||
|
||||
$key = q/rinW;MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="53" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="|."$dir".q|img70.png"
|
||||
ALT="$r \in W$">|;
|
||||
|
||||
$key = q/theta=0;MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="45" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="|."$dir".q|img86.png"
|
||||
ALT="$\theta = 0$">|;
|
||||
|
||||
$key = q/{displaymath}Ax=b,{displaymath};MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="57" HEIGHT="30" BORDER="0"
|
||||
SRC="|."$dir".q|img1.png"
|
||||
ALT="\begin{displaymath}
|
||||
Ax=b,
|
||||
\end{displaymath}">|;
|
||||
|
||||
$key = q/Re^{n_i^delta};MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="32" HEIGHT="24" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="|."$dir".q|img23.png"
|
||||
ALT="$\Re^{n_i^\delta}$">|;
|
||||
|
||||
$key = q/R_CinRe^{n_Ctimesn};MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="101" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="|."$dir".q|img46.png"
|
||||
ALT="$R_C \in \Re^{n_C \times n}$">|;
|
||||
|
||||
$key = q/y;MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="14" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="|."$dir".q|img96.png"
|
||||
ALT="$y$">|;
|
||||
|
||||
$key = q/{displaymath}A_C=R_CAR_C^T{displaymath};MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="109" HEIGHT="31" BORDER="0"
|
||||
SRC="|."$dir".q|img47.png"
|
||||
ALT="\begin{displaymath}
|
||||
A_C=R_C A R_C^T
|
||||
\end{displaymath}">|;
|
||||
|
||||
$key = q/l;MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="10" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="|."$dir".q|img62.png"
|
||||
ALT="$l$">|;
|
||||
|
||||
$key = q/v_i=R_i^{delta}v;MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="71" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="|."$dir".q|img29.png"
|
||||
ALT="$v_i = R_i^{\delta} v$">|;
|
||||
|
||||
$key = q/N_r;MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="26" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="|."$dir".q|img69.png"
|
||||
ALT="$N_r$">|;
|
||||
|
||||
$key = q/P_C=R_C^T;MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="75" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="|."$dir".q|img75.png"
|
||||
ALT="$P_C=R_C^T$">|;
|
||||
|
||||
$key = q/{displaymath}M_{2LH-PRE}^{-1}=M_{C}^{-1}+left(I-M_{C}^{-1}Aright)M_{1L}^{-1}.{displaymath};MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="308" HEIGHT="33" BORDER="0"
|
||||
SRC="|."$dir".q|img56.png"
|
||||
ALT="\begin{displaymath}
|
||||
M_{2LH-PRE}^{-1} = M_{C}^{-1} + \left( I - M_{C}^{-1}A \right) M_{1L}^{-1}.
|
||||
\end{displaymath}">|;
|
||||
|
||||
$key = q/v_i^{delta}inRe^{n_i^delta};MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="70" HEIGHT="43" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="|."$dir".q|img20.png"
|
||||
ALT="$v_i^{\delta} \in \Re^{n_i^\delta}$">|;
|
||||
|
||||
$key = q/{displaymath}M_{RAS}^{-1}=sum_{i=1}^m(tilde{R}_i^0)^T(A_i^delta)^{-1}R_i^{delta}.{displaymath};MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="216" HEIGHT="58" BORDER="0"
|
||||
SRC="|."$dir".q|img40.png"
|
||||
ALT="\begin{displaymath}
|
||||
M_{RAS}^{-1}= \sum_{i=1}^m (\tilde{R}_i^0)^T
|
||||
(A_i^\delta)^{-1} R_i^{\delta}.
|
||||
\end{displaymath}">|;
|
||||
|
||||
$key = q/A_l;MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="22" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="|."$dir".q|img63.png"
|
||||
ALT="$A_l$">|;
|
||||
|
||||
$key = q/n_C;MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="26" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="|."$dir".q|img45.png"
|
||||
ALT="$n_C$">|;
|
||||
|
||||
$key = q/W_i^delta;MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="30" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="|."$dir".q|img17.png"
|
||||
ALT="$W_i^\delta$">|;
|
||||
|
||||
$key = q/A_i^delta;MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="25" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="|."$dir".q|img28.png"
|
||||
ALT="$A_i^\delta$">|;
|
||||
|
||||
$key = q/{displaymath}M_{AS}^{-1}=sum_{i=1}^m(R_i^{delta})^T(A_i^delta)^{-1}R_i^{delta},{displaymath};MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="206" HEIGHT="58" BORDER="0"
|
||||
SRC="|."$dir".q|img27.png"
|
||||
ALT="\begin{displaymath}
|
||||
M_{AS}^{-1}= \sum_{i=1}^m (R_i^{\delta})^T
|
||||
(A_i^\delta)^{-1} R_i^{\delta},
|
||||
\end{displaymath}">|;
|
||||
|
||||
$key = q/delta>0;MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="45" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="|."$dir".q|img8.png"
|
||||
ALT="$\delta > 0$">|;
|
||||
|
||||
$key = q/w_i;MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="23" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="|."$dir".q|img32.png"
|
||||
ALT="$w_i$">|;
|
||||
|
||||
$key = q/w=sum_{i=1}^m(R_i^{delta})^Tw_i;MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="144" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="|."$dir".q|img33.png"
|
||||
ALT="$w = \sum_{i=1}^m (R_i^{\delta})^T w_i$">|;
|
||||
|
||||
$key = q/p;MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="13" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="|."$dir".q|img34.png"
|
||||
ALT="$p$">|;
|
||||
|
||||
$key = q/A_i^delta=R_i^deltaA(R_i^delta)^TinRe^{n_i^deltatimesn_i^delta};MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="201" HEIGHT="43" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="|."$dir".q|img25.png"
|
||||
ALT="$A_i^\delta=R_i^\delta A (R_i^\delta)^T \in
|
||||
\Re^{n_i^\delta \times n_i^\delta}$">|;
|
||||
|
||||
$key = q/thetain[0,1];MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="69" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="|."$dir".q|img72.png"
|
||||
ALT="$\theta \in [0,1]$">|;
|
||||
|
||||
$key = q/A=(a_{ij})inRe^{ntimesn};MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="137" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="|."$dir".q|img3.png"
|
||||
ALT="$A=(a_{ij}) \in \Re^{n \times n}$">|;
|
||||
|
||||
$key = q/tilde{R}_i^0;MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="25" HEIGHT="42" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="|."$dir".q|img37.png"
|
||||
ALT="$\tilde{R}_i^0$">|;
|
||||
|
||||
$key = q/M_{2L-A}^{-1};MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="59" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="|."$dir".q|img53.png"
|
||||
ALT="$M_{2L-A}^{-1}$">|;
|
||||
|
||||
$key = q/{displaymath}P_C=SP,{displaymath};MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="73" HEIGHT="30" BORDER="0"
|
||||
SRC="|."$dir".q|img81.png"
|
||||
ALT="\begin{displaymath}
|
||||
P_C = S P,
|
||||
\end{displaymath}">|;
|
||||
|
||||
$key = q/M_{C};MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="32" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="|."$dir".q|img51.png"
|
||||
ALT="$M_{C}$">|;
|
||||
|
||||
$key = q/{displaymath}N_r=left{sinW:|a_{rs}|>thetasqrt{|a_{rr}a_{ss}|}right}cupleft{rright},{displaymath};MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="319" HEIGHT="38" BORDER="0"
|
||||
SRC="|."$dir".q|img71.png"
|
||||
ALT="\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\} ,
|
||||
\end{displaymath}">|;
|
||||
|
||||
$key = q/R_i^{delta};MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="25" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="|."$dir".q|img22.png"
|
||||
ALT="$R_i^{\delta}$">|;
|
||||
|
||||
$key = q/R_C;MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="29" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="|."$dir".q|img67.png"
|
||||
ALT="$R_C$">|;
|
||||
|
||||
$key = q/>0;MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="32" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="|."$dir".q|img92.png"
|
||||
ALT="$>0$">|;
|
||||
|
||||
$key = q/(tilde{R}_i^0)^TinRe^{n_i^deltatimesn};MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="118" HEIGHT="43" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="|."$dir".q|img36.png"
|
||||
ALT="$(\tilde{R}_i^0)^T \in \Re^{n_i^\delta \times n}$">|;
|
||||
|
||||
$key = q/A_1=A;MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="61" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="|."$dir".q|img65.png"
|
||||
ALT="$A_1=A$">|;
|
||||
|
||||
$key = q/M;MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="23" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="|."$dir".q|img59.png"
|
||||
ALT="$M$">|;
|
||||
|
||||
$key = q/x;MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="14" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="|."$dir".q|img95.png"
|
||||
ALT="$x$">|;
|
||||
|
||||
$key = q/G=(W,E);MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="93" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="|."$dir".q|img4.png"
|
||||
ALT="$G=(W,E)$">|;
|
||||
|
||||
$key = q/{displaymath}array{{l}w=M_{1L}^{-1}v,z=w+M_{C}^{-1}(v-Aw);array{{displaymath};MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="177" HEIGHT="51" BORDER="0"
|
||||
SRC="|."$dir".q|img55.png"
|
||||
ALT="\begin{displaymath}
|
||||
\begin{array}{l}
|
||||
w = M_{1L}^{-1} v, \\\\
|
||||
z = w + M_{C}^{-1} (v-Aw);
|
||||
\end{array}\end{displaymath}">|;
|
||||
|
||||
$key = q/P;MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="18" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="|."$dir".q|img79.png"
|
||||
ALT="$P$">|;
|
||||
|
||||
$key = q/A_C;MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="29" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="|."$dir".q|img43.png"
|
||||
ALT="$A_C$">|;
|
||||
|
||||
$key = q/n_i^delta;MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="22" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="|."$dir".q|img16.png"
|
||||
ALT="$n_i^\delta$">|;
|
||||
|
||||
$key = q/M^{-1});MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="48" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="|."$dir".q|img99.png"
|
||||
ALT="$M^{-1})$">|;
|
||||
|
||||
$key = q/{displaymath}M_{C}^{-1}=R_C^TA_C^{-1}R_C,{displaymath};MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="144" HEIGHT="32" BORDER="0"
|
||||
SRC="|."$dir".q|img49.png"
|
||||
ALT="\begin{displaymath}
|
||||
M_{C}^{-1}= R_C^T A_C^{-1} R_C,
|
||||
\end{displaymath}">|;
|
||||
|
||||
$key = q/i;MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="10" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="|."$dir".q|img73.png"
|
||||
ALT="$i$">|;
|
||||
|
||||
$key = q/R_i^{delta}inRe^{n_i^deltatimesn};MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="93" HEIGHT="43" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="|."$dir".q|img18.png"
|
||||
ALT="$R_i^{\delta} \in
|
||||
\Re^{n_i^\delta \times n}$">|;
|
||||
|
||||
$key = q/in[0,1];MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="56" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="|."$dir".q|img90.png"
|
||||
ALT="$\in [0, 1]$">|;
|
||||
|
||||
$key = q/{displaymath}array{{l}w=M_{C}^{-1}v,z=w+M_{1L}^{-1}(v-Aw),array{{displaymath};MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="177" HEIGHT="51" BORDER="0"
|
||||
SRC="|."$dir".q|img57.png"
|
||||
ALT="\begin{displaymath}
|
||||
\begin{array}{l}
|
||||
w = M_{C}^{-1} v , \\\\
|
||||
z = w + M_{1L}^{-1} (v-Aw) ,
|
||||
\end{array}\end{displaymath}">|;
|
||||
|
||||
$key = q/p,t;MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="27" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="|."$dir".q|img35.png"
|
||||
ALT="$p,t$">|;
|
||||
|
||||
$key = q/Re^n;MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="26" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="|."$dir".q|img24.png"
|
||||
ALT="$\Re^n$">|;
|
||||
|
||||
$key = q/t;MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="11" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="|."$dir".q|img89.png"
|
||||
ALT="$t$">|;
|
||||
|
||||
$key = q/PinRe^{ntimesn_C};MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="90" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="|."$dir".q|img76.png"
|
||||
ALT="$P \in \Re^{n \times n_C}$">|;
|
||||
|
||||
$key = q/S;MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="16" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="|."$dir".q|img82.png"
|
||||
ALT="$S$">|;
|
||||
|
||||
$key = q/D^{-1}A;MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="50" HEIGHT="21" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="|."$dir".q|img85.png"
|
||||
ALT="$D^{-1}A$">|;
|
||||
|
||||
$key = q/M_{C}^{-1};MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="42" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="|."$dir".q|img50.png"
|
||||
ALT="$M_{C}^{-1}$">|;
|
||||
|
||||
$key = q/v;MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="|."$dir".q|img21.png"
|
||||
ALT="$v$">|;
|
||||
|
||||
$key = q/R_C^T;MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="29" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="|."$dir".q|img68.png"
|
||||
ALT="$R_C^T$">|;
|
||||
|
||||
$key = q/delta;MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="13" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="|."$dir".q|img9.png"
|
||||
ALT="$\delta$">|;
|
||||
|
||||
$key = q/ge0;MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="32" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="|."$dir".q|img88.png"
|
||||
ALT="$\ge 0$">|;
|
||||
|
||||
$key = q/{displaymath}M_{2LH-POST}^{-1}=M_{1L}^{-1}+left(I-M_{1L}^{-1}Aright)M_{C}^{-1}.{displaymath};MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="317" HEIGHT="33" BORDER="0"
|
||||
SRC="|."$dir".q|img58.png"
|
||||
ALT="\begin{displaymath}
|
||||
M_{2LH-POST}^{-1} = M_{1L}^{-1} + \left( I - M_{1L}^{-1}A \right) M_{C}^{-1}.
|
||||
\end{displaymath}">|;
|
||||
|
||||
$key = q/op;MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="22" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="|."$dir".q|img94.png"
|
||||
ALT="$op$">|;
|
||||
|
||||
$key = q/G;MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="18" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="|."$dir".q|img7.png"
|
||||
ALT="$G$">|;
|
||||
|
||||
$key = q/omega;MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="|."$dir".q|img84.png"
|
||||
ALT="$\omega$">|;
|
||||
|
||||
$key = q/P_C;MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="27" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="|."$dir".q|img78.png"
|
||||
ALT="$P_C$">|;
|
||||
|
||||
$key = q/W_C;MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="32" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="|."$dir".q|img44.png"
|
||||
ALT="$W_C$">|;
|
||||
|
||||
$key = q/W_i^0;MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="31" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="|."$dir".q|img74.png"
|
||||
ALT="$W_i^0$">|;
|
||||
|
||||
$key = q/op(M^{-1})=M^{-1};MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="132" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="|."$dir".q|img97.png"
|
||||
ALT="$op(M^{-1}) = M^{-1}$">|;
|
||||
|
||||
$key = q/W={1,2,ldots,n};MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="138" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="|."$dir".q|img5.png"
|
||||
ALT="$W=\{1, 2, \ldots, n\}$">|;
|
||||
|
||||
$key = q/framebox{minipage{{.85textwidth}{smalltabbing{quad=quad=quad=quad[-1mm]{v_1=v{;[{>{y_l=y_l+r_l{textbf{endfor}[1mm]{w=y_1{;tabbing{}minipage{};MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="430" HEIGHT="435" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="|."$dir".q|img66.png"
|
||||
ALT="\framebox{
|
||||
\begin{minipage}{.85\textwidth} {\small
|
||||
\begin{tabbing}
|
||||
\quad \=\quad...
|
||||
...= y_l+r_l$\\\\
|
||||
\textbf{endfor} [1mm]
|
||||
$w = y_1$;
|
||||
\end{tabbing}}
|
||||
\end{minipage}}">|;
|
||||
|
||||
$key = q/A;MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="18" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="|."$dir".q|img2.png"
|
||||
ALT="$A$">|;
|
||||
|
||||
$key = q/i=1,ldots,m;MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="97" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="|."$dir".q|img30.png"
|
||||
ALT="$i=1,\ldots,m$">|;
|
||||
|
||||
$key = q/y=op(M^{-1}),x;MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="117" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="|."$dir".q|img93.png"
|
||||
ALT="$y = op(M^{-1}) x$">|;
|
||||
|
||||
$key = q/{displaymath}S=I-omegaD^{-1}A,{displaymath};MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="126" HEIGHT="30" BORDER="0"
|
||||
SRC="|."$dir".q|img83.png"
|
||||
ALT="\begin{displaymath}
|
||||
S = I - \omega D^{-1} A ,
|
||||
\end{displaymath}">|;
|
||||
|
||||
$key = q/SinRe^{ntimesn};MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="78" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="|."$dir".q|img80.png"
|
||||
ALT="$S \in \Re^{n \times n}$">|;
|
||||
|
||||
$key = q/theta;MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="13" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="|."$dir".q|img91.png"
|
||||
ALT="$\theta$">|;
|
||||
|
||||
$key = q/{displaymath}M_{ASH}^{-1}=sum_{i=1}^m(R_i^{delta})^T(A_i^delta)^{-1}tilde{R}_i^0.{displaymath};MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="218" HEIGHT="58" BORDER="0"
|
||||
SRC="|."$dir".q|img41.png"
|
||||
ALT="\begin{displaymath}M_{ASH}^{-1}= \sum_{i=1}^m (R_i^{\delta})^T
|
||||
(A_i^\delta)^{-1} \tilde{R}_i^0.
|
||||
\end{displaymath}">|;
|
||||
|
||||
$key = q/op(M^{-1})=M^{-C};MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="136" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="|."$dir".q|img100.png"
|
||||
ALT="$op(M^{-1}) = M^{-C}$">|;
|
||||
|
||||
$key = q/W_i^deltasupsetW_i^{delta-1};MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="97" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="|."$dir".q|img14.png"
|
||||
ALT="$W_i^\delta \supset W_i^{\delta-1}$">|;
|
||||
|
||||
$key = q/vinRe^n;MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="56" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="|."$dir".q|img19.png"
|
||||
ALT="$v \in \Re^n$">|;
|
||||
|
||||
$key = q/W_i^deltabackslashW_i^0;MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="66" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
|
||||
SRC="|."$dir".q|img39.png"
|
||||
ALT="$W_i^\delta \backslash W_i^0$">|;
|
||||
|
||||
$key = q/m;MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="20" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
|
||||
SRC="|."$dir".q|img11.png"
|
||||
ALT="$m$">|;
|
||||
|
||||
$key = q/{displaymath}P=(p_{ij}),quadp_{ij}=left{array{{ll}1&quadmbox{if};iinV^j_C0&quadmbox{otherwise}array{right..{displaymath};MSF=1.6;LFS=11;AAT/;
|
||||
$cached_env_img{$key} = q|<IMG
|
||||
WIDTH="290" HEIGHT="52" BORDER="0"
|
||||
SRC="|."$dir".q|img77.png"
|
||||
ALT="\begin{displaymath}
|
||||
P=(p_{ij}), \quad p_{ij}=
|
||||
\left\{ \begin{array}{ll}
|
||||
1 & \qu...
|
||||
...\in V^j_C \\\\
|
||||
0 & \quad \mbox{otherwise}
|
||||
\end{array} \right. .
|
||||
\end{displaymath}">|;
|
||||
|
||||
1;
|
||||
|
||||
@ -0,0 +1,874 @@
|
||||
\batchmode
|
||||
\documentclass[a4paper,twoside,11pt]{article}
|
||||
|
||||
\usepackage{pstricks}
|
||||
\usepackage{fancybox}
|
||||
\usepackage{amsfonts}
|
||||
\usepackage{ifpdf}
|
||||
\usepackage[bookmarks=true, bookmarksnumbered=true, bookmarksopen=false, plainpages=false, pdfpagelabels, colorlinks, linkcolor=blue]{hyperref}
|
||||
\usepackage{ifthen}
|
||||
\usepackage{graphicx}
|
||||
|
||||
\newtheorem{theorem}{Theorem}
|
||||
\newtheorem{corollary}{Corollary} \usepackage{rotating}
|
||||
|
||||
|
||||
\pdfoutput=0
|
||||
|
||||
|
||||
|
||||
\setlength \textwidth{1.15\textwidth}
|
||||
\pagestyle{myheadings}
|
||||
|
||||
|
||||
|
||||
\newcounter{subroutine}[subsection]
|
||||
\newcounter{example}[subroutine] \makeatletter%
|
||||
\providecommand{\subsubroutine}[2]{%
|
||||
\stepcounter{subroutine}%
|
||||
\subsection*{\flushleft #1---#2 \endflushleft}%
|
||||
\addcontentsline{toc}{subsubsection}{#1}%
|
||||
\markright{#1}}%%
|
||||
\providecommand{\examplename}{Example}%
|
||||
\providecommand{\syntaxname}{Syntax}
|
||||
|
||||
\makeatother%
|
||||
\providecommand{\example}{\stepcounter{example}%
|
||||
\section*{Example~\arabic{example}}}
|
||||
|
||||
%
|
||||
\providecommand{\precdata}{\hyperlink{precdata}{{\tt mld\_prec\_type}}}%
|
||||
\providecommand{\descdata}{\hyperlink{descdata}{{\tt psb\_desc\_type}}}%
|
||||
\providecommand{\spdata}{\hyperlink{spdata}{{\tt psb\_spmat\_type}}}%
|
||||
\providecommand{\Ref}[1]{\mbox{(\ref{#1})}}
|
||||
|
||||
|
||||
|
||||
\usepackage[dvips]{pstcol}
|
||||
|
||||
|
||||
\pagecolor[gray]{.7}
|
||||
|
||||
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|
||||
|
||||
|
||||
|
||||
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|
||||
|
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|
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|
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|
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|
||||
\expandafter\renewcommand\csname #1\endcsname}%
|
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|
||||
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|
||||
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|
||||
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|
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|
||||
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|
||||
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|
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|
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|
||||
\addtolength{\textheight}{\topmargin}\setlength{\topmargin}{0pt}
|
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\addtolength{\textheight}{\headheight}\setlength{\headheight}{0pt}
|
||||
\addtolength{\textheight}{\headsep}\setlength{\headsep}{0pt}
|
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|
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|
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|
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|
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|
||||
\parindent=0pt\abovedisplayskip=0pt\belowdisplayskip=0pt}%
|
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\def\phantompar{\csname par\endcsname}\normalsize}%
|
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|
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\newcommand\lthtmlhboxmathA{\adjustnormalsize\setbox\sizebox=\hbox\bgroup\kern.05em }%
|
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|
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|
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\expandafter\box\next\egroup}%
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\ifdim\dimen0>.95\vsize
|
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\lthtmltypeout{%
|
||||
*** image for \lthtmlmathenv\space is too tall at \the\dimen0, reducing to .95 vsize ***}%
|
||||
\ht\sizebox.95\vsize \dp\sizebox\z@ \fi
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\lthtmltypeout{l2hSize %
|
||||
:\lthtmlmathenv:\the\ht\sizebox::\the\dp\sizebox::\the\wd\sizebox.\preveqno}}%
|
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\lthtmlmathtype{#1}\lthtmlvboxmathA}%
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\let\@savefreelist\@freelist \lthtmlhboxmathB}%
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\newcommand\lthtmlpictureZ[1]{\hfill\lthtmlfigureZ}%
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||||
\newcommand\lthtmlfigureZ{\lthtmlboxmathZ\lthtmllogmath\copy\sizebox
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\global\let\@freelist\@savefreelist}%
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\newcommand\lthtmldisplayA{\bgroup\catcode`\_=8 \lthtmldisplayAi}%
|
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\newcommand\lthtmldisplayAi[1]{\lthtmlmathtype{#1}\egroup\lthtmlvboxmathA}%
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\newcommand\lthtmldisplayB[1]{\edef\preveqno{(\theequation)}%
|
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\lthtmldisplayA{#1}\let\@eqnnum\relax}%
|
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\newcommand\lthtmldisplayZ{\lthtmlboxmathZ\lthtmllogmath\lthtmlsetmath}%
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\newcommand\lthtmlinlinemathA{\bgroup\catcode`\_=8 \lthtmlinlinemathB}
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\newcommand\lthtmlinlinemathB[1]{\lthtmlmathtype{#1}\egroup\lthtmlhboxmathA
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\vrule height1.5ex width0pt }%
|
||||
\newcommand\lthtmlinlineA{\bgroup\catcode`\_=8 \lthtmlinlineB}%
|
||||
\newcommand\lthtmlinlineB[1]{\lthtmlmathtype{#1}\egroup\lthtmlhboxmathA}%
|
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\newcommand\lthtmlinlineZ{\egroup\expandafter\ifdim\dp\sizebox>0pt %
|
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\expandafter\centerinlinemath\fi\lthtmllogmath\lthtmlsetinline}
|
||||
\newcommand\lthtmlinlinemathZ{\egroup\expandafter\ifdim\dp\sizebox>0pt %
|
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\expandafter\centerinlinemath\fi\lthtmllogmath\lthtmlsetmath}
|
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|
||||
\centerinlinemath\lthtmllogmath\lthtmlsetmath}
|
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\def\lthtmlsetinline{\hbox{\vrule width.1em \vtop{\vbox{%
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||||
\kern.1em\copy\sizebox}\ifdim\dp\sizebox>0pt\kern.1em\else\kern.3pt\fi
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\ifdim\hsize>\wd\sizebox \hrule depth1pt\fi}}}
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\def\lthtmlsetmath{\hbox{\vrule width.1em\kern-.05em\vtop{\vbox{%
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\kern.1em\kern0.8 pt\hbox{\hglue.17em\copy\sizebox\hglue0.8 pt}}\kern.3pt%
|
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|
||||
\ifdim\hsize>\wd\sizebox \hrule depth1pt\fi}}}
|
||||
\def\centerinlinemath{%
|
||||
\dimen1=\ifdim\ht\sizebox<\dp\sizebox \dp\sizebox\else\ht\sizebox\fi
|
||||
\advance\dimen1by.5pt \vrule width0pt height\dimen1 depth\dimen1
|
||||
\dp\sizebox=\dimen1\ht\sizebox=\dimen1\relax}
|
||||
|
||||
\def\lthtmlcheckvsize{\ifdim\ht\sizebox<\vsize
|
||||
\ifdim\wd\sizebox<\hsize\expandafter\hfill\fi \expandafter\vfill
|
||||
\else\expandafter\vss\fi}%
|
||||
\providecommand{\selectlanguage}[1]{}%
|
||||
\makeatletter \tracingstats = 1
|
||||
|
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|
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\begin{document}
|
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|
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\lthtmltypeout{latex2htmlLength hsize=\the\hsize}\lthtmltypeout{}%
|
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\lthtmltypeout{latex2htmlLength vsize=\the\vsize}\lthtmltypeout{}%
|
||||
\lthtmltypeout{latex2htmlLength hoffset=\the\hoffset}\lthtmltypeout{}%
|
||||
\lthtmltypeout{latex2htmlLength voffset=\the\voffset}\lthtmltypeout{}%
|
||||
\lthtmltypeout{latex2htmlLength topmargin=\the\topmargin}\lthtmltypeout{}%
|
||||
\lthtmltypeout{latex2htmlLength topskip=\the\topskip}\lthtmltypeout{}%
|
||||
\lthtmltypeout{latex2htmlLength headheight=\the\headheight}\lthtmltypeout{}%
|
||||
\lthtmltypeout{latex2htmlLength headsep=\the\headsep}\lthtmltypeout{}%
|
||||
\lthtmltypeout{latex2htmlLength parskip=\the\parskip}\lthtmltypeout{}%
|
||||
\lthtmltypeout{latex2htmlLength oddsidemargin=\the\oddsidemargin}\lthtmltypeout{}%
|
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\makeatletter
|
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\if@twoside\lthtmltypeout{latex2htmlLength evensidemargin=\the\evensidemargin}%
|
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\else\lthtmltypeout{latex2htmlLength evensidemargin=\the\oddsidemargin}\fi%
|
||||
\lthtmltypeout{}%
|
||||
\makeatother
|
||||
\setcounter{page}{1}
|
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\onecolumn
|
||||
|
||||
% !!! IMAGES START HERE !!!
|
||||
|
||||
|
||||
|
||||
\newlength{\centeroffset}%
|
||||
|
||||
\begingroup
|
||||
\renewcommand{\thepage}{toc}
|
||||
\endgroup
|
||||
\stepcounter{section}
|
||||
{\newpage\clearpage
|
||||
\lthtmldisplayA{displaymath238}%
|
||||
\begin{displaymath}
|
||||
Ax=b,
|
||||
\end{displaymath}%
|
||||
\lthtmldisplayZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
{\newpage\clearpage
|
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\lthtmlinlinemathA{tex2html_wrap_inline265}%
|
||||
$A$%
|
||||
\lthtmlinlinemathZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
\stepcounter{section}
|
||||
\stepcounter{section}
|
||||
\stepcounter{section}
|
||||
\stepcounter{subsection}
|
||||
\stepcounter{subsection}
|
||||
\stepcounter{subsection}
|
||||
\stepcounter{subsection}
|
||||
\stepcounter{section}
|
||||
\stepcounter{subsection}
|
||||
{\newpage\clearpage
|
||||
\lthtmlinlinemathA{tex2html_wrap_inline586}%
|
||||
$A=(a_{ij}) \in \Re^{n \times n}$%
|
||||
\lthtmlinlinemathZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
{\newpage\clearpage
|
||||
\lthtmlinlinemathA{tex2html_wrap_inline588}%
|
||||
$G=(W,E)$%
|
||||
\lthtmlinlinemathZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
{\newpage\clearpage
|
||||
\lthtmlinlinemathA{tex2html_wrap_inline592}%
|
||||
$W=\{1, 2, \ldots, n\}$%
|
||||
\lthtmlinlinemathZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
{\newpage\clearpage
|
||||
\lthtmlinlinemathA{tex2html_wrap_inline594}%
|
||||
$E=\{(i,j) : a_{ij} \neq 0\}$%
|
||||
\lthtmlinlinemathZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
{\newpage\clearpage
|
||||
\lthtmlinlinemathA{tex2html_wrap_inline596}%
|
||||
$G$%
|
||||
\lthtmlinlinemathZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
{\newpage\clearpage
|
||||
\lthtmlinlinemathA{tex2html_wrap_inline598}%
|
||||
$\delta > 0$%
|
||||
\lthtmlinlinemathZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
{\newpage\clearpage
|
||||
\lthtmlinlinemathA{tex2html_wrap_inline600}%
|
||||
$\delta$%
|
||||
\lthtmlinlinemathZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
{\newpage\clearpage
|
||||
\lthtmlinlinemathA{tex2html_wrap_inline602}%
|
||||
$W$%
|
||||
\lthtmlinlinemathZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
{\newpage\clearpage
|
||||
\lthtmlinlinemathA{tex2html_wrap_inline606}%
|
||||
$m$%
|
||||
\lthtmlinlinemathZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
{\newpage\clearpage
|
||||
\lthtmlinlinemathA{tex2html_wrap_inline608}%
|
||||
$W_i^0 \subset W$%
|
||||
\lthtmlinlinemathZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
{\newpage\clearpage
|
||||
\lthtmlinlinemathA{tex2html_wrap_inline610}%
|
||||
$\cup_{i=1}^m W_i^0 = W$%
|
||||
\lthtmlinlinemathZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
{\newpage\clearpage
|
||||
\lthtmlinlinemathA{tex2html_wrap_inline616}%
|
||||
$W_i^\delta \supset W_i^{\delta-1}$%
|
||||
\lthtmlinlinemathZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
{\newpage\clearpage
|
||||
\lthtmlinlinemathA{tex2html_wrap_inline618}%
|
||||
$W_i^{\delta-1}$%
|
||||
\lthtmlinlinemathZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
{\newpage\clearpage
|
||||
\lthtmlinlinemathA{tex2html_wrap_inline620}%
|
||||
$n_i^\delta$%
|
||||
\lthtmlinlinemathZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
{\newpage\clearpage
|
||||
\lthtmlinlinemathA{tex2html_wrap_inline622}%
|
||||
$W_i^\delta$%
|
||||
\lthtmlinlinemathZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
{\newpage\clearpage
|
||||
\lthtmlinlinemathA{tex2html_wrap_inline624}%
|
||||
$R_i^{\delta} \in
|
||||
\Re^{n_i^\delta \times n}$%
|
||||
\lthtmlinlinemathZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
{\newpage\clearpage
|
||||
\lthtmlinlinemathA{tex2html_wrap_inline626}%
|
||||
$v \in \Re^n$%
|
||||
\lthtmlinlinemathZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
{\newpage\clearpage
|
||||
\lthtmlinlinemathA{tex2html_wrap_inline628}%
|
||||
$v_i^{\delta} \in \Re^{n_i^\delta}$%
|
||||
\lthtmlinlinemathZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
{\newpage\clearpage
|
||||
\lthtmlinlinemathA{tex2html_wrap_inline630}%
|
||||
$v$%
|
||||
\lthtmlinlinemathZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
{\newpage\clearpage
|
||||
\lthtmlinlinemathA{tex2html_wrap_inline634}%
|
||||
$R_i^{\delta}$%
|
||||
\lthtmlinlinemathZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
{\newpage\clearpage
|
||||
\lthtmlinlinemathA{tex2html_wrap_inline636}%
|
||||
$\Re^{n_i^\delta}$%
|
||||
\lthtmlinlinemathZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
{\newpage\clearpage
|
||||
\lthtmlinlinemathA{tex2html_wrap_inline638}%
|
||||
$\Re^n$%
|
||||
\lthtmlinlinemathZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
{\newpage\clearpage
|
||||
\lthtmlinlinemathA{tex2html_wrap_inline640}%
|
||||
$A_i^\delta=R_i^\delta A (R_i^\delta)^T \in
|
||||
\Re^{n_i^\delta \times n_i^\delta}$%
|
||||
\lthtmlinlinemathZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
{\newpage\clearpage
|
||||
\lthtmlinlinemathA{tex2html_wrap_inline644}%
|
||||
$W_i^{\delta}$%
|
||||
\lthtmlinlinemathZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
{\newpage\clearpage
|
||||
\lthtmldisplayA{displaymath564}%
|
||||
\begin{displaymath}
|
||||
M_{AS}^{-1}= \sum_{i=1}^m (R_i^{\delta})^T
|
||||
(A_i^\delta)^{-1} R_i^{\delta},
|
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\end{displaymath}%
|
||||
\lthtmldisplayZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
{\newpage\clearpage
|
||||
\lthtmlinlinemathA{tex2html_wrap_inline646}%
|
||||
$A_i^\delta$%
|
||||
\lthtmlinlinemathZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
{\newpage\clearpage
|
||||
\lthtmlinlinemathA{tex2html_wrap_inline652}%
|
||||
$v_i = R_i^{\delta} v$%
|
||||
\lthtmlinlinemathZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
{\newpage\clearpage
|
||||
\lthtmlinlinemathA{tex2html_wrap_inline654}%
|
||||
$i=1,\ldots,m$%
|
||||
\lthtmlinlinemathZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
{\newpage\clearpage
|
||||
\lthtmlinlinemathA{tex2html_wrap_inline656}%
|
||||
$A_i^\delta w_i = v_i$%
|
||||
\lthtmlinlinemathZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
{\newpage\clearpage
|
||||
\lthtmlinlinemathA{tex2html_wrap_inline660}%
|
||||
$w_i$%
|
||||
\lthtmlinlinemathZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
{\newpage\clearpage
|
||||
\lthtmlinlinemathA{tex2html_wrap_inline662}%
|
||||
$w = \sum_{i=1}^m (R_i^{\delta})^T w_i$%
|
||||
\lthtmlinlinemathZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
{\newpage\clearpage
|
||||
\lthtmlinlinemathA{tex2html_wrap_inline664}%
|
||||
$p$%
|
||||
\lthtmlinlinemathZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
{\newpage\clearpage
|
||||
\lthtmlinlinemathA{tex2html_wrap_inline668}%
|
||||
$p,t$%
|
||||
\lthtmlinlinemathZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
{\newpage\clearpage
|
||||
\lthtmlinlinemathA{tex2html_wrap_inline672}%
|
||||
$(\tilde{R}_i^0)^T \in \Re^{n_i^\delta \times n}$%
|
||||
\lthtmlinlinemathZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
{\newpage\clearpage
|
||||
\lthtmlinlinemathA{tex2html_wrap_inline674}%
|
||||
$\tilde{R}_i^0$%
|
||||
\lthtmlinlinemathZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
{\newpage\clearpage
|
||||
\lthtmlinlinemathA{tex2html_wrap_inline676}%
|
||||
$R_i^\delta$%
|
||||
\lthtmlinlinemathZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
{\newpage\clearpage
|
||||
\lthtmlinlinemathA{tex2html_wrap_inline678}%
|
||||
$W_i^\delta \backslash W_i^0$%
|
||||
\lthtmlinlinemathZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
{\newpage\clearpage
|
||||
\lthtmldisplayA{displaymath565}%
|
||||
\begin{displaymath}
|
||||
M_{RAS}^{-1}= \sum_{i=1}^m (\tilde{R}_i^0)^T
|
||||
(A_i^\delta)^{-1} R_i^{\delta}.
|
||||
\end{displaymath}%
|
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\lthtmldisplayZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
{\newpage\clearpage
|
||||
\lthtmldisplayA{displaymath566}%
|
||||
\begin{displaymath} M_{ASH}^{-1}= \sum_{i=1}^m (R_i^{\delta})^T
|
||||
(A_i^\delta)^{-1} \tilde{R}_i^0.
|
||||
\end{displaymath}%
|
||||
\lthtmldisplayZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
{\newpage\clearpage
|
||||
\lthtmlinlinemathA{tex2html_wrap_inline680}%
|
||||
$\delta=0$%
|
||||
\lthtmlinlinemathZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
{\newpage\clearpage
|
||||
\lthtmlinlinemathA{tex2html_wrap_inline686}%
|
||||
$A_C$%
|
||||
\lthtmlinlinemathZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
{\newpage\clearpage
|
||||
\lthtmlinlinemathA{tex2html_wrap_inline692}%
|
||||
$W_C$%
|
||||
\lthtmlinlinemathZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
{\newpage\clearpage
|
||||
\lthtmlinlinemathA{tex2html_wrap_inline694}%
|
||||
$n_C$%
|
||||
\lthtmlinlinemathZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
{\newpage\clearpage
|
||||
\lthtmlinlinemathA{tex2html_wrap_inline696}%
|
||||
$R_C \in \Re^{n_C \times n}$%
|
||||
\lthtmlinlinemathZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
{\newpage\clearpage
|
||||
\lthtmldisplayA{displaymath567}%
|
||||
\begin{displaymath}
|
||||
A_C=R_C A R_C^T
|
||||
\end{displaymath}%
|
||||
\lthtmldisplayZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
{\newpage\clearpage
|
||||
\lthtmlinlinemathA{tex2html_wrap_inline700}%
|
||||
$M_{1L}$%
|
||||
\lthtmlinlinemathZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
{\newpage\clearpage
|
||||
\lthtmldisplayA{displaymath568}%
|
||||
\begin{displaymath}
|
||||
M_{C}^{-1}= R_C^T A_C^{-1} R_C,
|
||||
\end{displaymath}%
|
||||
\lthtmldisplayZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
{\newpage\clearpage
|
||||
\lthtmlinlinemathA{tex2html_wrap_inline704}%
|
||||
$M_{C}^{-1}$%
|
||||
\lthtmlinlinemathZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
{\newpage\clearpage
|
||||
\lthtmlinlinemathA{tex2html_wrap_inline710}%
|
||||
$M_{C}$%
|
||||
\lthtmlinlinemathZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
{\newpage\clearpage
|
||||
\lthtmldisplayA{displaymath569}%
|
||||
\begin{displaymath}
|
||||
M_{2LA}^{-1} = M_{C}^{-1} + M_{1L}^{-1}.
|
||||
\end{displaymath}%
|
||||
\lthtmldisplayZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
{\newpage\clearpage
|
||||
\lthtmlinlinemathA{tex2html_wrap_inline714}%
|
||||
$M_{2L-A}^{-1}$%
|
||||
\lthtmlinlinemathZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
{\newpage\clearpage
|
||||
\lthtmlinlinemathA{tex2html_wrap_inline720}%
|
||||
$M_{1L}^{-1}$%
|
||||
\lthtmlinlinemathZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
{\newpage\clearpage
|
||||
\lthtmldisplayA{displaymath570}%
|
||||
\begin{displaymath}
|
||||
\begin{array}{l}
|
||||
w = M_{1L}^{-1} v, \\
|
||||
z = w + M_{C}^{-1} (v-Aw);
|
||||
\end{array}
|
||||
\end{displaymath}%
|
||||
\lthtmldisplayZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
{\newpage\clearpage
|
||||
\lthtmldisplayA{displaymath571}%
|
||||
\begin{displaymath}
|
||||
M_{2LH-PRE}^{-1} = M_{C}^{-1} + \left( I - M_{C}^{-1}A \right) M_{1L}^{-1}.
|
||||
\end{displaymath}%
|
||||
\lthtmldisplayZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
{\newpage\clearpage
|
||||
\lthtmldisplayA{displaymath572}%
|
||||
\begin{displaymath}
|
||||
\begin{array}{l}
|
||||
w = M_{C}^{-1} v , \\
|
||||
z = w + M_{1L}^{-1} (v-Aw) ,
|
||||
\end{array}
|
||||
\end{displaymath}%
|
||||
\lthtmldisplayZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
{\newpage\clearpage
|
||||
\lthtmldisplayA{displaymath573}%
|
||||
\begin{displaymath}
|
||||
M_{2LH-POST}^{-1} = M_{1L}^{-1} + \left( I - M_{1L}^{-1}A \right) M_{C}^{-1}.
|
||||
\end{displaymath}%
|
||||
\lthtmldisplayZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
{\newpage\clearpage
|
||||
\lthtmlinlinemathA{tex2html_wrap_inline734}%
|
||||
$M$%
|
||||
\lthtmlinlinemathZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
{\newpage\clearpage
|
||||
\lthtmlinlinemathA{tex2html_wrap_inline738}%
|
||||
$w=M^{-1}v$%
|
||||
\lthtmlinlinemathZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
{\newpage\clearpage
|
||||
\lthtmlinlinemathA{tex2html_wrap_inline740}%
|
||||
$nlev$%
|
||||
\lthtmlinlinemathZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
{\newpage\clearpage
|
||||
\lthtmlinlinemathA{tex2html_wrap_inline742}%
|
||||
$l$%
|
||||
\lthtmlinlinemathZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
{\newpage\clearpage
|
||||
\lthtmlinlinemathA{tex2html_wrap_inline744}%
|
||||
$A_l$%
|
||||
\lthtmlinlinemathZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
{\newpage\clearpage
|
||||
\lthtmlinlinemathA{tex2html_wrap_inline746}%
|
||||
$M_l$%
|
||||
\lthtmlinlinemathZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
{\newpage\clearpage
|
||||
\lthtmlinlinemathA{tex2html_wrap_inline748}%
|
||||
$A_1=A$%
|
||||
\lthtmlinlinemathZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
{\newpage\clearpage
|
||||
\lthtmlpictureA{tex2html_wrap860}%
|
||||
\framebox{
|
||||
\begin{minipage}{.85\textwidth} {\small
|
||||
\begin{tabbing}
|
||||
\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]
|
||||
\textbf{endfor} \\[2mm]
|
||||
! apply the coarsest-level correction\\[1mm]
|
||||
$y_{nlev} = A_{nlev}^{-1} v_{nlev}$\\[2mm]
|
||||
\textbf{for $l=nlev -1 , 1, -1$\ do}\\[1mm]
|
||||
\> ! transfer $y_{l+1}$\ to the next finer level\\
|
||||
\> $y_l = R_{l+1}^T y_{l+1}$;\\[1mm]
|
||||
\> ! compute the residual at the current level\\
|
||||
\> $r_l = v_l-A_l^{-1} y_l$;\\[1mm]
|
||||
\> ! apply the basic Schwarz preconditioner to the residual\\
|
||||
\> $r_l = M_l^{-1} r_l$\\[1mm]
|
||||
\> ! update $y_l$\\
|
||||
\> $y_l = y_l+r_l$\\
|
||||
\textbf{endfor} \\[1mm]
|
||||
$w = y_1$;
|
||||
\end{tabbing}
|
||||
}
|
||||
\end{minipage}
|
||||
}%
|
||||
\lthtmlpictureZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
\stepcounter{subsection}
|
||||
{\newpage\clearpage
|
||||
\lthtmlinlinemathA{tex2html_wrap_inline776}%
|
||||
$R_C$%
|
||||
\lthtmlinlinemathZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
{\newpage\clearpage
|
||||
\lthtmlinlinemathA{tex2html_wrap_inline784}%
|
||||
$R_C^T$%
|
||||
\lthtmlinlinemathZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
{\newpage\clearpage
|
||||
\lthtmlinlinemathA{tex2html_wrap_inline798}%
|
||||
$N_r$%
|
||||
\lthtmlinlinemathZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
{\newpage\clearpage
|
||||
\lthtmlinlinemathA{tex2html_wrap_inline802}%
|
||||
$r \in W$%
|
||||
\lthtmlinlinemathZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
{\newpage\clearpage
|
||||
\lthtmldisplayA{displaymath574}%
|
||||
\begin{displaymath} N_r = \left\{s \in W: |a_{rs}| > \theta \sqrt{|a_{rr}a_{ss}|} \right\}
|
||||
\cup \left\{ r \right\} ,
|
||||
\end{displaymath}%
|
||||
\lthtmldisplayZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
{\newpage\clearpage
|
||||
\lthtmlinlinemathA{tex2html_wrap_inline804}%
|
||||
$\theta \in [0,1]$%
|
||||
\lthtmlinlinemathZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
{\newpage\clearpage
|
||||
\lthtmlinlinemathA{tex2html_wrap_inline806}%
|
||||
$i$%
|
||||
\lthtmlinlinemathZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
{\newpage\clearpage
|
||||
\lthtmlinlinemathA{tex2html_wrap_inline808}%
|
||||
$W_i^0$%
|
||||
\lthtmlinlinemathZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
{\newpage\clearpage
|
||||
\lthtmlinlinemathA{tex2html_wrap_inline812}%
|
||||
$P_C=R_C^T$%
|
||||
\lthtmlinlinemathZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
{\newpage\clearpage
|
||||
\lthtmlinlinemathA{tex2html_wrap_inline814}%
|
||||
$P \in \Re^{n \times n_C}$%
|
||||
\lthtmlinlinemathZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
{\newpage\clearpage
|
||||
\lthtmldisplayA{displaymath531}%
|
||||
\begin{displaymath}
|
||||
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. .
|
||||
\end{displaymath}%
|
||||
\lthtmldisplayZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
{\newpage\clearpage
|
||||
\lthtmlinlinemathA{tex2html_wrap_inline816}%
|
||||
$P_C$%
|
||||
\lthtmlinlinemathZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
{\newpage\clearpage
|
||||
\lthtmlinlinemathA{tex2html_wrap_inline818}%
|
||||
$P$%
|
||||
\lthtmlinlinemathZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
{\newpage\clearpage
|
||||
\lthtmlinlinemathA{tex2html_wrap_inline820}%
|
||||
$S \in \Re^{n \times n}$%
|
||||
\lthtmlinlinemathZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
{\newpage\clearpage
|
||||
\lthtmldisplayA{displaymath542}%
|
||||
\begin{displaymath}
|
||||
P_C = S P,
|
||||
\end{displaymath}%
|
||||
\lthtmldisplayZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
{\newpage\clearpage
|
||||
\lthtmlinlinemathA{tex2html_wrap_inline822}%
|
||||
$S$%
|
||||
\lthtmlinlinemathZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
{\newpage\clearpage
|
||||
\lthtmldisplayA{displaymath546}%
|
||||
\begin{displaymath}
|
||||
S = I - \omega D^{-1} A ,
|
||||
\end{displaymath}%
|
||||
\lthtmldisplayZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
{\newpage\clearpage
|
||||
\lthtmlinlinemathA{tex2html_wrap_inline824}%
|
||||
$\omega$%
|
||||
\lthtmlinlinemathZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
{\newpage\clearpage
|
||||
\lthtmlinlinemathA{tex2html_wrap_inline826}%
|
||||
$D^{-1}A$%
|
||||
\lthtmlinlinemathZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
\stepcounter{section}
|
||||
{\newpage\clearpage
|
||||
\lthtmlinlinemathA{tex2html_wrap_inline983}%
|
||||
$\theta = 0$%
|
||||
\lthtmlinlinemathZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
\stepcounter{subsection}
|
||||
\stepcounter{section}
|
||||
{\newpage\clearpage
|
||||
\lthtmlinlinemathA{tex2html_wrap_inline1324}%
|
||||
$w$%
|
||||
\lthtmlinlinemathZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
\stepcounter{subsection}
|
||||
\stepcounter{subsection}
|
||||
{\newpage\clearpage
|
||||
\lthtmlinlinemathA{tex2html_wrap_inline1328}%
|
||||
$\ge 0$%
|
||||
\lthtmlinlinemathZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
{\newpage\clearpage
|
||||
\lthtmlinlinemathA{tex2html_wrap_inline1342}%
|
||||
$t$%
|
||||
\lthtmlinlinemathZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
{\newpage\clearpage
|
||||
\lthtmlinlinemathA{tex2html_wrap_inline1346}%
|
||||
$\in [0, 1]$%
|
||||
\lthtmlinlinemathZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
{\newpage\clearpage
|
||||
\lthtmlinlinemathA{tex2html_wrap_inline1348}%
|
||||
$\theta$%
|
||||
\lthtmlinlinemathZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
{\newpage\clearpage
|
||||
\lthtmlinlinemathA{tex2html_wrap_inline1352}%
|
||||
$>0$%
|
||||
\lthtmlinlinemathZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
\stepcounter{subsection}
|
||||
\stepcounter{subsection}
|
||||
{\newpage\clearpage
|
||||
\lthtmlinlinemathA{tex2html_wrap_inline1374}%
|
||||
$y = op(M^{-1})\, x$%
|
||||
\lthtmlinlinemathZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
{\newpage\clearpage
|
||||
\lthtmlinlinemathA{tex2html_wrap_inline1378}%
|
||||
$op$%
|
||||
\lthtmlinlinemathZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
{\newpage\clearpage
|
||||
\lthtmlinlinemathA{tex2html_wrap_inline1382}%
|
||||
$x$%
|
||||
\lthtmlinlinemathZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
{\newpage\clearpage
|
||||
\lthtmlinlinemathA{tex2html_wrap_inline1384}%
|
||||
$y$%
|
||||
\lthtmlinlinemathZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
{\newpage\clearpage
|
||||
\lthtmlinlinemathA{tex2html_wrap_inline1386}%
|
||||
$op(M^{-1}) = M^{-1}$%
|
||||
\lthtmlinlinemathZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
{\newpage\clearpage
|
||||
\lthtmlinlinemathA{tex2html_wrap_inline1388}%
|
||||
$op(M^{-1}) = M^{-T}$%
|
||||
\lthtmlinlinemathZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
{\newpage\clearpage
|
||||
\lthtmlinlinemathA{tex2html_wrap_inline1390}%
|
||||
$M^{-1})$%
|
||||
\lthtmlinlinemathZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
{\newpage\clearpage
|
||||
\lthtmlinlinemathA{tex2html_wrap_inline1392}%
|
||||
$op(M^{-1}) = M^{-C}$%
|
||||
\lthtmlinlinemathZ
|
||||
\lthtmlcheckvsize\clearpage}
|
||||
|
||||
\stepcounter{subsection}
|
||||
\stepcounter{subsection}
|
||||
\stepcounter{section}
|
||||
\appendix
|
||||
\stepcounter{section}
|
||||
|
||||
\end{document}
|
||||
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Reference in New Issue