mld2p4:
docs/html/WARNINGS docs/html/images.aux docs/html/images.log docs/html/images.out docs/html/images.pl docs/html/images.tex Doc fixes: take out aux files from html subdir.stopcriterion
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This is pdfTeXk, Version 3.141592-1.40.3 (Web2C 7.5.6) (format=latex 2008.5.20) 23 JUL 2008 10:16
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|
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]
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l2hSize :tex2html_wrap_inline820:7.48248pt::0.0pt::9.09842pt.
|
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[79
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]
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l2hSize :tex2html_wrap_inline822:9.30704pt::9.30704pt::46.61087pt.
|
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[80
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|
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]
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l2hSize :displaymath544:15.72917pt::0.0pt::349.0pt.
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[81
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]
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l2hSize :tex2html_wrap_inline824:7.48248pt::0.0pt::7.89314pt.
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]
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l2hSize :displaymath548:15.72917pt::0.0pt::349.0pt.
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[83
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]
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l2hSize :tex2html_wrap_inline826:7.07185pt::0.0pt::7.75627pt.
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]
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l2hSize :tex2html_wrap_inline828:9.12923pt::0.0pt::29.49117pt.
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]
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l2hSize :tex2html_wrap_inline985:7.60416pt::0.0pt::26.06703pt.
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]
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l2hSize :tex2html_wrap_inline1316:7.07185pt::0.0pt::8.68147pt.
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l2hSize :tex2html_wrap_inline1320:7.57185pt::7.57185pt::17.58084pt.
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|
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]
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l2hSize :tex2html_wrap_inline1334:7.07185pt::0.0pt::4.50171pt.
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|
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]
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l2hSize :tex2html_wrap_inline1338:8.7125pt::8.7125pt::32.78915pt.
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|
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]
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l2hSize :tex2html_wrap_inline1340:7.60416pt::0.0pt::5.99211pt.
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|
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]
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l2hSize :tex2html_wrap_inline1346:9.62923pt::9.62923pt::75.59969pt.
|
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[92
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|
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|
|
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]
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l2hSize :tex2html_wrap_inline1362:7.57185pt::7.57185pt::17.58084pt.
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[93
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]
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l2hSize :tex2html_wrap_inline1374:9.62923pt::9.62923pt::71.50383pt.
|
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[94
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|
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|
|
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]
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l2hSize :tex2html_wrap_inline1378:7.57185pt::7.57185pt::11.36446pt.
|
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[95
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|
|
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|
|
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]
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|
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l2hSize :tex2html_wrap_inline1382:7.07185pt::0.0pt::6.80576pt.
|
|
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[96
|
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|
|
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|
|
||||||
]
|
|
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l2hSize :tex2html_wrap_inline1384:7.57185pt::7.57185pt::6.30898pt.
|
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[97
|
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|
|
||||||
|
|
||||||
]
|
|
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l2hSize :tex2html_wrap_inline1386:9.62923pt::9.62923pt::80.83733pt.
|
|
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[98
|
|
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|
|
||||||
|
|
||||||
]
|
|
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l2hSize :tex2html_wrap_inline1388:9.94032pt::9.94032pt::82.71652pt.
|
|
||||||
[99
|
|
||||||
|
|
||||||
|
|
||||||
]
|
|
||||||
l2hSize :tex2html_wrap_inline1390:9.62923pt::9.62923pt::27.98401pt.
|
|
||||||
[100
|
|
||||||
|
|
||||||
|
|
||||||
]
|
|
||||||
l2hSize :tex2html_wrap_inline1392:9.94032pt::9.94032pt::83.21068pt.
|
|
||||||
[101
|
|
||||||
|
|
||||||
|
|
||||||
] (./images.aux) )
|
|
||||||
Here is how much of TeX's memory you used:
|
|
||||||
4373 strings out of 94074
|
|
||||||
57907 string characters out of 1167173
|
|
||||||
141384 words of memory out of 1500000
|
|
||||||
7590 multiletter control sequences out of 10000+50000
|
|
||||||
10304 words of font info for 41 fonts, out of 1200000 for 2000
|
|
||||||
645 hyphenation exceptions out of 8191
|
|
||||||
30i,8n,37p,306b,390s stack positions out of 5000i,500n,6000p,200000b,10000s
|
|
||||||
|
|
||||||
Output written on images.dvi (101 pages, 72868 bytes).
|
|
@ -1,663 +0,0 @@
|
|||||||
# 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="|."$dir".q|img99.png"
|
|
||||||
ALT="$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="13" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
|
|
||||||
SRC="|."$dir".q|img97.png"
|
|
||||||
ALT="$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/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/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/{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="31" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
|
|
||||||
SRC="|."$dir".q|img93.png"
|
|
||||||
ALT="$> 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="15" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
|
|
||||||
SRC="|."$dir".q|img96.png"
|
|
||||||
ALT="$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="|."$dir".q|img100.png"
|
|
||||||
ALT="$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/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/{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/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="21" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
|
|
||||||
SRC="|."$dir".q|img95.png"
|
|
||||||
ALT="$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/4slash(3||D^{-1}A||_infty);MSF=1.6;LFS=11;AAT/;
|
|
||||||
$cached_env_img{$key} = q|<IMG
|
|
||||||
WIDTH="124" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
|
|
||||||
SRC="|."$dir".q|img92.png"
|
|
||||||
ALT="$4/(3\vert\vert D^{-1}A\vert\vert _\infty)$">|;
|
|
||||||
|
|
||||||
$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="|."$dir".q|img98.png"
|
|
||||||
ALT="$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="118" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
|
|
||||||
SRC="|."$dir".q|img94.png"
|
|
||||||
ALT="$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="|."$dir".q|img101.png"
|
|
||||||
ALT="$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;
|
|
||||||
|
|
@ -1,980 +0,0 @@
|
|||||||
\nonstopmode
|
|
||||||
\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}
|
|
||||||
|
|
||||||
\usepackage[latin1]{inputenc}
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
\makeatletter
|
|
||||||
|
|
||||||
\makeatletter
|
|
||||||
\count@=\the\catcode`\_ \catcode`\_=8
|
|
||||||
\newenvironment{tex2html_wrap}{}{}%
|
|
||||||
\catcode`\<=12\catcode`\_=\count@
|
|
||||||
\newcommand{\providedcommand}[1]{\expandafter\providecommand\csname #1\endcsname}%
|
|
||||||
\newcommand{\renewedcommand}[1]{\expandafter\providecommand\csname #1\endcsname{}%
|
|
||||||
\expandafter\renewcommand\csname #1\endcsname}%
|
|
||||||
\newcommand{\newedenvironment}[1]{\newenvironment{#1}{}{}\renewenvironment{#1}}%
|
|
||||||
\let\newedcommand\renewedcommand
|
|
||||||
\let\renewedenvironment\newedenvironment
|
|
||||||
\makeatother
|
|
||||||
\let\mathon=$
|
|
||||||
\let\mathoff=$
|
|
||||||
\ifx\AtBeginDocument\undefined \newcommand{\AtBeginDocument}[1]{}\fi
|
|
||||||
\newbox\sizebox
|
|
||||||
\setlength{\hoffset}{0pt}\setlength{\voffset}{0pt}
|
|
||||||
\addtolength{\textheight}{\footskip}\setlength{\footskip}{0pt}
|
|
||||||
\addtolength{\textheight}{\topmargin}\setlength{\topmargin}{0pt}
|
|
||||||
\addtolength{\textheight}{\headheight}\setlength{\headheight}{0pt}
|
|
||||||
\addtolength{\textheight}{\headsep}\setlength{\headsep}{0pt}
|
|
||||||
\setlength{\textwidth}{349pt}
|
|
||||||
\newwrite\lthtmlwrite
|
|
||||||
\makeatletter
|
|
||||||
\let\realnormalsize=\normalsize
|
|
||||||
\global\topskip=2sp
|
|
||||||
\def\preveqno{}\let\real@float=\@float \let\realend@float=\end@float
|
|
||||||
\def\@float{\let\@savefreelist\@freelist\real@float}
|
|
||||||
\def\liih@math{\ifmmode$\else\bad@math\fi}
|
|
||||||
\def\end@float{\realend@float\global\let\@freelist\@savefreelist}
|
|
||||||
\let\real@dbflt=\@dbflt \let\end@dblfloat=\end@float
|
|
||||||
\let\@largefloatcheck=\relax
|
|
||||||
\let\if@boxedmulticols=\iftrue
|
|
||||||
\def\@dbflt{\let\@savefreelist\@freelist\real@dbflt}
|
|
||||||
\def\adjustnormalsize{\def\normalsize{\mathsurround=0pt \realnormalsize
|
|
||||||
\parindent=0pt\abovedisplayskip=0pt\belowdisplayskip=0pt}%
|
|
||||||
\def\phantompar{\csname par\endcsname}\normalsize}%
|
|
||||||
\def\lthtmltypeout#1{{\let\protect\string \immediate\write\lthtmlwrite{#1}}}%
|
|
||||||
\newcommand\lthtmlhboxmathA{\adjustnormalsize\setbox\sizebox=\hbox\bgroup\kern.05em }%
|
|
||||||
\newcommand\lthtmlhboxmathB{\adjustnormalsize\setbox\sizebox=\hbox to\hsize\bgroup\hfill }%
|
|
||||||
\newcommand\lthtmlvboxmathA{\adjustnormalsize\setbox\sizebox=\vbox\bgroup %
|
|
||||||
\let\ifinner=\iffalse \let\)\liih@math }%
|
|
||||||
\newcommand\lthtmlboxmathZ{\@next\next\@currlist{}{\def\next{\voidb@x}}%
|
|
||||||
\expandafter\box\next\egroup}%
|
|
||||||
\newcommand\lthtmlmathtype[1]{\gdef\lthtmlmathenv{#1}}%
|
|
||||||
\newcommand\lthtmllogmath{\dimen0\ht\sizebox \advance\dimen0\dp\sizebox
|
|
||||||
\ifdim\dimen0>.95\vsize
|
|
||||||
\lthtmltypeout{%
|
|
||||||
*** image for \lthtmlmathenv\space is too tall at \the\dimen0, reducing to .95 vsize ***}%
|
|
||||||
\ht\sizebox.95\vsize \dp\sizebox\z@ \fi
|
|
||||||
\lthtmltypeout{l2hSize %
|
|
||||||
:\lthtmlmathenv:\the\ht\sizebox::\the\dp\sizebox::\the\wd\sizebox.\preveqno}}%
|
|
||||||
\newcommand\lthtmlfigureA[1]{\let\@savefreelist\@freelist
|
|
||||||
\lthtmlmathtype{#1}\lthtmlvboxmathA}%
|
|
||||||
\newcommand\lthtmlpictureA{\bgroup\catcode`\_=8 \lthtmlpictureB}%
|
|
||||||
\newcommand\lthtmlpictureB[1]{\lthtmlmathtype{#1}\egroup
|
|
||||||
\let\@savefreelist\@freelist \lthtmlhboxmathB}%
|
|
||||||
\newcommand\lthtmlpictureZ[1]{\hfill\lthtmlfigureZ}%
|
|
||||||
\newcommand\lthtmlfigureZ{\lthtmlboxmathZ\lthtmllogmath\copy\sizebox
|
|
||||||
\global\let\@freelist\@savefreelist}%
|
|
||||||
\newcommand\lthtmldisplayA{\bgroup\catcode`\_=8 \lthtmldisplayAi}%
|
|
||||||
\newcommand\lthtmldisplayAi[1]{\lthtmlmathtype{#1}\egroup\lthtmlvboxmathA}%
|
|
||||||
\newcommand\lthtmldisplayB[1]{\edef\preveqno{(\theequation)}%
|
|
||||||
\lthtmldisplayA{#1}\let\@eqnnum\relax}%
|
|
||||||
\newcommand\lthtmldisplayZ{\lthtmlboxmathZ\lthtmllogmath\lthtmlsetmath}%
|
|
||||||
\newcommand\lthtmlinlinemathA{\bgroup\catcode`\_=8 \lthtmlinlinemathB}
|
|
||||||
\newcommand\lthtmlinlinemathB[1]{\lthtmlmathtype{#1}\egroup\lthtmlhboxmathA
|
|
||||||
\vrule height1.5ex width0pt }%
|
|
||||||
\newcommand\lthtmlinlineA{\bgroup\catcode`\_=8 \lthtmlinlineB}%
|
|
||||||
\newcommand\lthtmlinlineB[1]{\lthtmlmathtype{#1}\egroup\lthtmlhboxmathA}%
|
|
||||||
\newcommand\lthtmlinlineZ{\egroup\expandafter\ifdim\dp\sizebox>0pt %
|
|
||||||
\expandafter\centerinlinemath\fi\lthtmllogmath\lthtmlsetinline}
|
|
||||||
\newcommand\lthtmlinlinemathZ{\egroup\expandafter\ifdim\dp\sizebox>0pt %
|
|
||||||
\expandafter\centerinlinemath\fi\lthtmllogmath\lthtmlsetmath}
|
|
||||||
\newcommand\lthtmlindisplaymathZ{\egroup %
|
|
||||||
\centerinlinemath\lthtmllogmath\lthtmlsetmath}
|
|
||||||
\def\lthtmlsetinline{\hbox{\vrule width.1em \vtop{\vbox{%
|
|
||||||
\kern.1em\copy\sizebox}\ifdim\dp\sizebox>0pt\kern.1em\else\kern.3pt\fi
|
|
||||||
\ifdim\hsize>\wd\sizebox \hrule depth1pt\fi}}}
|
|
||||||
\def\lthtmlsetmath{\hbox{\vrule width.1em\kern-.05em\vtop{\vbox{%
|
|
||||||
\kern.1em\kern0.8 pt\hbox{\hglue.17em\copy\sizebox\hglue0.8 pt}}\kern.3pt%
|
|
||||||
\ifdim\dp\sizebox>0pt\kern.1em\fi \kern0.8 pt%
|
|
||||||
\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
|
|
||||||
|
|
||||||
|
|
||||||
\begin{document}
|
|
||||||
\pagestyle{empty}\thispagestyle{empty}\lthtmltypeout{}%
|
|
||||||
\lthtmltypeout{latex2htmlLength hsize=\the\hsize}\lthtmltypeout{}%
|
|
||||||
\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{}%
|
|
||||||
\makeatletter
|
|
||||||
\if@twoside\lthtmltypeout{latex2htmlLength evensidemargin=\the\evensidemargin}%
|
|
||||||
\else\lthtmltypeout{latex2htmlLength evensidemargin=\the\oddsidemargin}\fi%
|
|
||||||
\lthtmltypeout{}%
|
|
||||||
\makeatother
|
|
||||||
\setcounter{page}{1}
|
|
||||||
\onecolumn
|
|
||||||
|
|
||||||
% !!! IMAGES START HERE !!!
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
\newlength{\centeroffset}%
|
|
||||||
|
|
||||||
\begingroup
|
|
||||||
\renewcommand{\thepage}{toc}
|
|
||||||
\endgroup
|
|
||||||
\stepcounter{section}
|
|
||||||
{\newpage\clearpage
|
|
||||||
% contents=begin{displaymath} Ax=b, end{displaymath}
|
|
||||||
\lthtmldisplayA{displaymath242}%
|
|
||||||
\begin{displaymath}
|
|
||||||
Ax=b,
|
|
||||||
\end{displaymath}%
|
|
||||||
\lthtmldisplayZ
|
|
||||||
\lthtmlcheckvsize\clearpage}
|
|
||||||
|
|
||||||
{\newpage\clearpage
|
|
||||||
% contents=$A$
|
|
||||||
\lthtmlinlinemathA{tex2html_wrap_inline268}%
|
|
||||||
$A$%
|
|
||||||
\lthtmlinlinemathZ
|
|
||||||
\lthtmlcheckvsize\clearpage}
|
|
||||||
|
|
||||||
\stepcounter{section}
|
|
||||||
\stepcounter{section}
|
|
||||||
\stepcounter{subsection}
|
|
||||||
\stepcounter{subsection}
|
|
||||||
\stepcounter{subsection}
|
|
||||||
\stepcounter{subsection}
|
|
||||||
\stepcounter{section}
|
|
||||||
\stepcounter{subsection}
|
|
||||||
{\newpage\clearpage
|
|
||||||
% contents=$A=(a_{ij}) \in \Re^{n \times n}$
|
|
||||||
\lthtmlinlinemathA{tex2html_wrap_inline588}%
|
|
||||||
$A=(a_{ij}) \in \Re^{n \times n}$%
|
|
||||||
\lthtmlinlinemathZ
|
|
||||||
\lthtmlcheckvsize\clearpage}
|
|
||||||
|
|
||||||
{\newpage\clearpage
|
|
||||||
% contents=$G=(W,E)$
|
|
||||||
\lthtmlinlinemathA{tex2html_wrap_inline590}%
|
|
||||||
$G=(W,E)$%
|
|
||||||
\lthtmlinlinemathZ
|
|
||||||
\lthtmlcheckvsize\clearpage}
|
|
||||||
|
|
||||||
{\newpage\clearpage
|
|
||||||
% contents=$W=\{1, 2, \ldots, n\}$
|
|
||||||
\lthtmlinlinemathA{tex2html_wrap_inline594}%
|
|
||||||
$W=\{1, 2, \ldots, n\}$%
|
|
||||||
\lthtmlinlinemathZ
|
|
||||||
\lthtmlcheckvsize\clearpage}
|
|
||||||
|
|
||||||
{\newpage\clearpage
|
|
||||||
% contents=$E=\{(i,j) : a_{ij} \neq 0\}$
|
|
||||||
\lthtmlinlinemathA{tex2html_wrap_inline596}%
|
|
||||||
$E=\{(i,j) : a_{ij} \neq 0\}$%
|
|
||||||
\lthtmlinlinemathZ
|
|
||||||
\lthtmlcheckvsize\clearpage}
|
|
||||||
|
|
||||||
{\newpage\clearpage
|
|
||||||
% contents=$G$
|
|
||||||
\lthtmlinlinemathA{tex2html_wrap_inline598}%
|
|
||||||
$G$%
|
|
||||||
\lthtmlinlinemathZ
|
|
||||||
\lthtmlcheckvsize\clearpage}
|
|
||||||
|
|
||||||
{\newpage\clearpage
|
|
||||||
% contents=$\delta > 0$
|
|
||||||
\lthtmlinlinemathA{tex2html_wrap_inline600}%
|
|
||||||
$\delta > 0$%
|
|
||||||
\lthtmlinlinemathZ
|
|
||||||
\lthtmlcheckvsize\clearpage}
|
|
||||||
|
|
||||||
{\newpage\clearpage
|
|
||||||
% contents=$\delta$
|
|
||||||
\lthtmlinlinemathA{tex2html_wrap_inline602}%
|
|
||||||
$\delta$%
|
|
||||||
\lthtmlinlinemathZ
|
|
||||||
\lthtmlcheckvsize\clearpage}
|
|
||||||
|
|
||||||
{\newpage\clearpage
|
|
||||||
% contents=$W$
|
|
||||||
\lthtmlinlinemathA{tex2html_wrap_inline604}%
|
|
||||||
$W$%
|
|
||||||
\lthtmlinlinemathZ
|
|
||||||
\lthtmlcheckvsize\clearpage}
|
|
||||||
|
|
||||||
{\newpage\clearpage
|
|
||||||
% contents=$m$
|
|
||||||
\lthtmlinlinemathA{tex2html_wrap_inline608}%
|
|
||||||
$m$%
|
|
||||||
\lthtmlinlinemathZ
|
|
||||||
\lthtmlcheckvsize\clearpage}
|
|
||||||
|
|
||||||
{\newpage\clearpage
|
|
||||||
% contents=$W_i^0 \subset W$
|
|
||||||
\lthtmlinlinemathA{tex2html_wrap_inline610}%
|
|
||||||
$W_i^0 \subset W$%
|
|
||||||
\lthtmlinlinemathZ
|
|
||||||
\lthtmlcheckvsize\clearpage}
|
|
||||||
|
|
||||||
{\newpage\clearpage
|
|
||||||
% contents=$\cup_{i=1}^m W_i^0 = W$
|
|
||||||
\lthtmlinlinemathA{tex2html_wrap_inline612}%
|
|
||||||
$\cup_{i=1}^m W_i^0 = W$%
|
|
||||||
\lthtmlinlinemathZ
|
|
||||||
\lthtmlcheckvsize\clearpage}
|
|
||||||
|
|
||||||
{\newpage\clearpage
|
|
||||||
% contents=$W_i^\delta \supset W_i^{\delta-1}$
|
|
||||||
\lthtmlinlinemathA{tex2html_wrap_inline618}%
|
|
||||||
$W_i^\delta \supset W_i^{\delta-1}$%
|
|
||||||
\lthtmlinlinemathZ
|
|
||||||
\lthtmlcheckvsize\clearpage}
|
|
||||||
|
|
||||||
{\newpage\clearpage
|
|
||||||
% contents=$W_i^{\delta-1}$
|
|
||||||
\lthtmlinlinemathA{tex2html_wrap_inline620}%
|
|
||||||
$W_i^{\delta-1}$%
|
|
||||||
\lthtmlinlinemathZ
|
|
||||||
\lthtmlcheckvsize\clearpage}
|
|
||||||
|
|
||||||
{\newpage\clearpage
|
|
||||||
% contents=$n_i^\delta$
|
|
||||||
\lthtmlinlinemathA{tex2html_wrap_inline622}%
|
|
||||||
$n_i^\delta$%
|
|
||||||
\lthtmlinlinemathZ
|
|
||||||
\lthtmlcheckvsize\clearpage}
|
|
||||||
|
|
||||||
{\newpage\clearpage
|
|
||||||
% contents=$W_i^\delta$
|
|
||||||
\lthtmlinlinemathA{tex2html_wrap_inline624}%
|
|
||||||
$W_i^\delta$%
|
|
||||||
\lthtmlinlinemathZ
|
|
||||||
\lthtmlcheckvsize\clearpage}
|
|
||||||
|
|
||||||
{\newpage\clearpage
|
|
||||||
% contents=$R_i^{\delta} \in \Re^{n_i^\delta \times n}$
|
|
||||||
\lthtmlinlinemathA{tex2html_wrap_inline626}%
|
|
||||||
$R_i^{\delta} \in
|
|
||||||
\Re^{n_i^\delta \times n}$%
|
|
||||||
\lthtmlinlinemathZ
|
|
||||||
\lthtmlcheckvsize\clearpage}
|
|
||||||
|
|
||||||
{\newpage\clearpage
|
|
||||||
% contents=$v \in \Re^n$
|
|
||||||
\lthtmlinlinemathA{tex2html_wrap_inline628}%
|
|
||||||
$v \in \Re^n$%
|
|
||||||
\lthtmlinlinemathZ
|
|
||||||
\lthtmlcheckvsize\clearpage}
|
|
||||||
|
|
||||||
{\newpage\clearpage
|
|
||||||
% contents=$v_i^{\delta} \in \Re^{n_i^\delta}$
|
|
||||||
\lthtmlinlinemathA{tex2html_wrap_inline630}%
|
|
||||||
$v_i^{\delta} \in \Re^{n_i^\delta}$%
|
|
||||||
\lthtmlinlinemathZ
|
|
||||||
\lthtmlcheckvsize\clearpage}
|
|
||||||
|
|
||||||
{\newpage\clearpage
|
|
||||||
% contents=$v$
|
|
||||||
\lthtmlinlinemathA{tex2html_wrap_inline632}%
|
|
||||||
$v$%
|
|
||||||
\lthtmlinlinemathZ
|
|
||||||
\lthtmlcheckvsize\clearpage}
|
|
||||||
|
|
||||||
{\newpage\clearpage
|
|
||||||
% contents=$R_i^{\delta}$
|
|
||||||
\lthtmlinlinemathA{tex2html_wrap_inline636}%
|
|
||||||
$R_i^{\delta}$%
|
|
||||||
\lthtmlinlinemathZ
|
|
||||||
\lthtmlcheckvsize\clearpage}
|
|
||||||
|
|
||||||
{\newpage\clearpage
|
|
||||||
% contents=$\Re^{n_i^\delta}$
|
|
||||||
\lthtmlinlinemathA{tex2html_wrap_inline638}%
|
|
||||||
$\Re^{n_i^\delta}$%
|
|
||||||
\lthtmlinlinemathZ
|
|
||||||
\lthtmlcheckvsize\clearpage}
|
|
||||||
|
|
||||||
{\newpage\clearpage
|
|
||||||
% contents=$\Re^n$
|
|
||||||
\lthtmlinlinemathA{tex2html_wrap_inline640}%
|
|
||||||
$\Re^n$%
|
|
||||||
\lthtmlinlinemathZ
|
|
||||||
\lthtmlcheckvsize\clearpage}
|
|
||||||
|
|
||||||
{\newpage\clearpage
|
|
||||||
% contents=$A_i^\delta=R_i^\delta A (R_i^\delta)^T \in \Re^{n_i^\delta \times n_i^\delta}$
|
|
||||||
\lthtmlinlinemathA{tex2html_wrap_inline642}%
|
|
||||||
$A_i^\delta=R_i^\delta A (R_i^\delta)^T \in
|
|
||||||
\Re^{n_i^\delta \times n_i^\delta}$%
|
|
||||||
\lthtmlinlinemathZ
|
|
||||||
\lthtmlcheckvsize\clearpage}
|
|
||||||
|
|
||||||
{\newpage\clearpage
|
|
||||||
% contents=$W_i^{\delta}$
|
|
||||||
\lthtmlinlinemathA{tex2html_wrap_inline646}%
|
|
||||||
$W_i^{\delta}$%
|
|
||||||
\lthtmlinlinemathZ
|
|
||||||
\lthtmlcheckvsize\clearpage}
|
|
||||||
|
|
||||||
{\newpage\clearpage
|
|
||||||
% contents=begin{displaymath} M_{AS}^{-1}= \sum_{i=1}^m (R_i^{\delta})^T (A_i^\delta)^{-1} R_i^{\delta}, end{displaymath}
|
|
||||||
\lthtmldisplayA{displaymath566}%
|
|
||||||
\begin{displaymath}
|
|
||||||
M_{AS}^{-1}= \sum_{i=1}^m (R_i^{\delta})^T
|
|
||||||
(A_i^\delta)^{-1} R_i^{\delta},
|
|
||||||
\end{displaymath}%
|
|
||||||
\lthtmldisplayZ
|
|
||||||
\lthtmlcheckvsize\clearpage}
|
|
||||||
|
|
||||||
{\newpage\clearpage
|
|
||||||
% contents=$A_i^\delta$
|
|
||||||
\lthtmlinlinemathA{tex2html_wrap_inline648}%
|
|
||||||
$A_i^\delta$%
|
|
||||||
\lthtmlinlinemathZ
|
|
||||||
\lthtmlcheckvsize\clearpage}
|
|
||||||
|
|
||||||
{\newpage\clearpage
|
|
||||||
% contents=$v_i = R_i^{\delta} v$
|
|
||||||
\lthtmlinlinemathA{tex2html_wrap_inline654}%
|
|
||||||
$v_i = R_i^{\delta} v$%
|
|
||||||
\lthtmlinlinemathZ
|
|
||||||
\lthtmlcheckvsize\clearpage}
|
|
||||||
|
|
||||||
{\newpage\clearpage
|
|
||||||
% contents=$i=1,\ldots,m$
|
|
||||||
\lthtmlinlinemathA{tex2html_wrap_inline656}%
|
|
||||||
$i=1,\ldots,m$%
|
|
||||||
\lthtmlinlinemathZ
|
|
||||||
\lthtmlcheckvsize\clearpage}
|
|
||||||
|
|
||||||
{\newpage\clearpage
|
|
||||||
% contents=$A_i^\delta w_i = v_i$
|
|
||||||
\lthtmlinlinemathA{tex2html_wrap_inline658}%
|
|
||||||
$A_i^\delta w_i = v_i$%
|
|
||||||
\lthtmlinlinemathZ
|
|
||||||
\lthtmlcheckvsize\clearpage}
|
|
||||||
|
|
||||||
{\newpage\clearpage
|
|
||||||
% contents=$w_i$
|
|
||||||
\lthtmlinlinemathA{tex2html_wrap_inline662}%
|
|
||||||
$w_i$%
|
|
||||||
\lthtmlinlinemathZ
|
|
||||||
\lthtmlcheckvsize\clearpage}
|
|
||||||
|
|
||||||
{\newpage\clearpage
|
|
||||||
% contents=$w = \sum_{i=1}^m (R_i^{\delta})^T w_i$
|
|
||||||
\lthtmlinlinemathA{tex2html_wrap_inline664}%
|
|
||||||
$w = \sum_{i=1}^m (R_i^{\delta})^T w_i$%
|
|
||||||
\lthtmlinlinemathZ
|
|
||||||
\lthtmlcheckvsize\clearpage}
|
|
||||||
|
|
||||||
{\newpage\clearpage
|
|
||||||
% contents=$p$
|
|
||||||
\lthtmlinlinemathA{tex2html_wrap_inline666}%
|
|
||||||
$p$%
|
|
||||||
\lthtmlinlinemathZ
|
|
||||||
\lthtmlcheckvsize\clearpage}
|
|
||||||
|
|
||||||
{\newpage\clearpage
|
|
||||||
% contents=$p,t$
|
|
||||||
\lthtmlinlinemathA{tex2html_wrap_inline670}%
|
|
||||||
$p,t$%
|
|
||||||
\lthtmlinlinemathZ
|
|
||||||
\lthtmlcheckvsize\clearpage}
|
|
||||||
|
|
||||||
{\newpage\clearpage
|
|
||||||
% contents=$(\tilde{R}_i^0)^T \in \Re^{n_i^\delta \times n}$
|
|
||||||
\lthtmlinlinemathA{tex2html_wrap_inline674}%
|
|
||||||
$(\tilde{R}_i^0)^T \in \Re^{n_i^\delta \times n}$%
|
|
||||||
\lthtmlinlinemathZ
|
|
||||||
\lthtmlcheckvsize\clearpage}
|
|
||||||
|
|
||||||
{\newpage\clearpage
|
|
||||||
% contents=$\tilde{R}_i^0$
|
|
||||||
\lthtmlinlinemathA{tex2html_wrap_inline676}%
|
|
||||||
$\tilde{R}_i^0$%
|
|
||||||
\lthtmlinlinemathZ
|
|
||||||
\lthtmlcheckvsize\clearpage}
|
|
||||||
|
|
||||||
{\newpage\clearpage
|
|
||||||
% contents=$R_i^\delta$
|
|
||||||
\lthtmlinlinemathA{tex2html_wrap_inline678}%
|
|
||||||
$R_i^\delta$%
|
|
||||||
\lthtmlinlinemathZ
|
|
||||||
\lthtmlcheckvsize\clearpage}
|
|
||||||
|
|
||||||
{\newpage\clearpage
|
|
||||||
% contents=$W_i^\delta \backslash W_i^0$
|
|
||||||
\lthtmlinlinemathA{tex2html_wrap_inline680}%
|
|
||||||
$W_i^\delta \backslash W_i^0$%
|
|
||||||
\lthtmlinlinemathZ
|
|
||||||
\lthtmlcheckvsize\clearpage}
|
|
||||||
|
|
||||||
{\newpage\clearpage
|
|
||||||
% contents=begin{displaymath} M_{RAS}^{-1}= \sum_{i=1}^m (\tilde{R}_i^0)^T (A_i^\delta)^{-1} R_i^{\delta}. end{displaymath}
|
|
||||||
\lthtmldisplayA{displaymath567}%
|
|
||||||
\begin{displaymath}
|
|
||||||
M_{RAS}^{-1}= \sum_{i=1}^m (\tilde{R}_i^0)^T
|
|
||||||
(A_i^\delta)^{-1} R_i^{\delta}.
|
|
||||||
\end{displaymath}%
|
|
||||||
\lthtmldisplayZ
|
|
||||||
\lthtmlcheckvsize\clearpage}
|
|
||||||
|
|
||||||
{\newpage\clearpage
|
|
||||||
% contents=begin{displaymath} M_{ASH}^{-1}= \sum_{i=1}^m (R_i^{\delta})^T (A_i^\delta)^{-1} \tilde{R}_i^0. end{displaymath}
|
|
||||||
\lthtmldisplayA{displaymath568}%
|
|
||||||
\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
|
|
||||||
% contents=$\delta=0$
|
|
||||||
\lthtmlinlinemathA{tex2html_wrap_inline682}%
|
|
||||||
$\delta=0$%
|
|
||||||
\lthtmlinlinemathZ
|
|
||||||
\lthtmlcheckvsize\clearpage}
|
|
||||||
|
|
||||||
{\newpage\clearpage
|
|
||||||
% contents=$A_C$
|
|
||||||
\lthtmlinlinemathA{tex2html_wrap_inline688}%
|
|
||||||
$A_C$%
|
|
||||||
\lthtmlinlinemathZ
|
|
||||||
\lthtmlcheckvsize\clearpage}
|
|
||||||
|
|
||||||
{\newpage\clearpage
|
|
||||||
% contents=$W_C$
|
|
||||||
\lthtmlinlinemathA{tex2html_wrap_inline694}%
|
|
||||||
$W_C$%
|
|
||||||
\lthtmlinlinemathZ
|
|
||||||
\lthtmlcheckvsize\clearpage}
|
|
||||||
|
|
||||||
{\newpage\clearpage
|
|
||||||
% contents=$n_C$
|
|
||||||
\lthtmlinlinemathA{tex2html_wrap_inline696}%
|
|
||||||
$n_C$%
|
|
||||||
\lthtmlinlinemathZ
|
|
||||||
\lthtmlcheckvsize\clearpage}
|
|
||||||
|
|
||||||
{\newpage\clearpage
|
|
||||||
% contents=$R_C \in \Re^{n_C \times n}$
|
|
||||||
\lthtmlinlinemathA{tex2html_wrap_inline698}%
|
|
||||||
$R_C \in \Re^{n_C \times n}$%
|
|
||||||
\lthtmlinlinemathZ
|
|
||||||
\lthtmlcheckvsize\clearpage}
|
|
||||||
|
|
||||||
{\newpage\clearpage
|
|
||||||
% contents=begin{displaymath} A_C=R_C A R_C^T end{displaymath}
|
|
||||||
\lthtmldisplayA{displaymath569}%
|
|
||||||
\begin{displaymath}
|
|
||||||
A_C=R_C A R_C^T
|
|
||||||
\end{displaymath}%
|
|
||||||
\lthtmldisplayZ
|
|
||||||
\lthtmlcheckvsize\clearpage}
|
|
||||||
|
|
||||||
{\newpage\clearpage
|
|
||||||
% contents=$M_{1L}$
|
|
||||||
\lthtmlinlinemathA{tex2html_wrap_inline702}%
|
|
||||||
$M_{1L}$%
|
|
||||||
\lthtmlinlinemathZ
|
|
||||||
\lthtmlcheckvsize\clearpage}
|
|
||||||
|
|
||||||
{\newpage\clearpage
|
|
||||||
% contents=begin{displaymath} M_{C}^{-1}= R_C^T A_C^{-1} R_C, end{displaymath}
|
|
||||||
\lthtmldisplayA{displaymath570}%
|
|
||||||
\begin{displaymath}
|
|
||||||
M_{C}^{-1}= R_C^T A_C^{-1} R_C,
|
|
||||||
\end{displaymath}%
|
|
||||||
\lthtmldisplayZ
|
|
||||||
\lthtmlcheckvsize\clearpage}
|
|
||||||
|
|
||||||
{\newpage\clearpage
|
|
||||||
% contents=$M_{C}^{-1}$
|
|
||||||
\lthtmlinlinemathA{tex2html_wrap_inline706}%
|
|
||||||
$M_{C}^{-1}$%
|
|
||||||
\lthtmlinlinemathZ
|
|
||||||
\lthtmlcheckvsize\clearpage}
|
|
||||||
|
|
||||||
{\newpage\clearpage
|
|
||||||
% contents=$M_{C}$
|
|
||||||
\lthtmlinlinemathA{tex2html_wrap_inline712}%
|
|
||||||
$M_{C}$%
|
|
||||||
\lthtmlinlinemathZ
|
|
||||||
\lthtmlcheckvsize\clearpage}
|
|
||||||
|
|
||||||
{\newpage\clearpage
|
|
||||||
% contents=begin{displaymath} M_{2LA}^{-1} = M_{C}^{-1} + M_{1L}^{-1}. end{displaymath}
|
|
||||||
\lthtmldisplayA{displaymath571}%
|
|
||||||
\begin{displaymath}
|
|
||||||
M_{2LA}^{-1} = M_{C}^{-1} + M_{1L}^{-1}.
|
|
||||||
\end{displaymath}%
|
|
||||||
\lthtmldisplayZ
|
|
||||||
\lthtmlcheckvsize\clearpage}
|
|
||||||
|
|
||||||
{\newpage\clearpage
|
|
||||||
% contents=$M_{2L-A}^{-1}$
|
|
||||||
\lthtmlinlinemathA{tex2html_wrap_inline716}%
|
|
||||||
$M_{2L-A}^{-1}$%
|
|
||||||
\lthtmlinlinemathZ
|
|
||||||
\lthtmlcheckvsize\clearpage}
|
|
||||||
|
|
||||||
{\newpage\clearpage
|
|
||||||
% contents=$M_{1L}^{-1}$
|
|
||||||
\lthtmlinlinemathA{tex2html_wrap_inline722}%
|
|
||||||
$M_{1L}^{-1}$%
|
|
||||||
\lthtmlinlinemathZ
|
|
||||||
\lthtmlcheckvsize\clearpage}
|
|
||||||
|
|
||||||
{\newpage\clearpage
|
|
||||||
% contents=begin{displaymath} begin{array}{l} w = M_{1L}^{-1} v, \\z = w + M_{C}^{-1} (v-Aw); end{array} end{displaymath}
|
|
||||||
\lthtmldisplayA{displaymath572}%
|
|
||||||
\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
|
|
||||||
% contents=begin{displaymath} M_{2LH-PRE}^{-1} = M_{C}^{-1} + \left( I - M_{C}^{-1}A \right) M_{1L}^{-1}. end{displaymath}
|
|
||||||
\lthtmldisplayA{displaymath573}%
|
|
||||||
\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
|
|
||||||
% contents=begin{displaymath} begin{array}{l} w = M_{C}^{-1} v , \\z = w + M_{1L}^{-1} (v-Aw) , end{array} end{displaymath}
|
|
||||||
\lthtmldisplayA{displaymath574}%
|
|
||||||
\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
|
|
||||||
% contents=begin{displaymath} M_{2LH-POST}^{-1} = M_{1L}^{-1} + \left( I - M_{1L}^{-1}A \right) M_{C}^{-1}. end{displaymath}
|
|
||||||
\lthtmldisplayA{displaymath575}%
|
|
||||||
\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
|
|
||||||
% contents=$M$
|
|
||||||
\lthtmlinlinemathA{tex2html_wrap_inline736}%
|
|
||||||
$M$%
|
|
||||||
\lthtmlinlinemathZ
|
|
||||||
\lthtmlcheckvsize\clearpage}
|
|
||||||
|
|
||||||
{\newpage\clearpage
|
|
||||||
% contents=$w=M^{-1}v$
|
|
||||||
\lthtmlinlinemathA{tex2html_wrap_inline740}%
|
|
||||||
$w=M^{-1}v$%
|
|
||||||
\lthtmlinlinemathZ
|
|
||||||
\lthtmlcheckvsize\clearpage}
|
|
||||||
|
|
||||||
{\newpage\clearpage
|
|
||||||
% contents=$nlev$
|
|
||||||
\lthtmlinlinemathA{tex2html_wrap_inline742}%
|
|
||||||
$nlev$%
|
|
||||||
\lthtmlinlinemathZ
|
|
||||||
\lthtmlcheckvsize\clearpage}
|
|
||||||
|
|
||||||
{\newpage\clearpage
|
|
||||||
% contents=$l$
|
|
||||||
\lthtmlinlinemathA{tex2html_wrap_inline744}%
|
|
||||||
$l$%
|
|
||||||
\lthtmlinlinemathZ
|
|
||||||
\lthtmlcheckvsize\clearpage}
|
|
||||||
|
|
||||||
{\newpage\clearpage
|
|
||||||
% contents=$A_l$
|
|
||||||
\lthtmlinlinemathA{tex2html_wrap_inline746}%
|
|
||||||
$A_l$%
|
|
||||||
\lthtmlinlinemathZ
|
|
||||||
\lthtmlcheckvsize\clearpage}
|
|
||||||
|
|
||||||
{\newpage\clearpage
|
|
||||||
% contents=$M_l$
|
|
||||||
\lthtmlinlinemathA{tex2html_wrap_inline748}%
|
|
||||||
$M_l$%
|
|
||||||
\lthtmlinlinemathZ
|
|
||||||
\lthtmlcheckvsize\clearpage}
|
|
||||||
|
|
||||||
{\newpage\clearpage
|
|
||||||
% contents=$A_1=A$
|
|
||||||
\lthtmlinlinemathA{tex2html_wrap_inline750}%
|
|
||||||
$A_1=A$%
|
|
||||||
\lthtmlinlinemathZ
|
|
||||||
\lthtmlcheckvsize\clearpage}
|
|
||||||
|
|
||||||
{\newpage\clearpage
|
|
||||||
% contents=\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 ...}
|
|
||||||
\lthtmlpictureA{tex2html_wrap862}%
|
|
||||||
\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
|
|
||||||
% contents=$R_C$
|
|
||||||
\lthtmlinlinemathA{tex2html_wrap_inline778}%
|
|
||||||
$R_C$%
|
|
||||||
\lthtmlinlinemathZ
|
|
||||||
\lthtmlcheckvsize\clearpage}
|
|
||||||
|
|
||||||
{\newpage\clearpage
|
|
||||||
% contents=$R_C^T$
|
|
||||||
\lthtmlinlinemathA{tex2html_wrap_inline786}%
|
|
||||||
$R_C^T$%
|
|
||||||
\lthtmlinlinemathZ
|
|
||||||
\lthtmlcheckvsize\clearpage}
|
|
||||||
|
|
||||||
{\newpage\clearpage
|
|
||||||
% contents=$N_r$
|
|
||||||
\lthtmlinlinemathA{tex2html_wrap_inline800}%
|
|
||||||
$N_r$%
|
|
||||||
\lthtmlinlinemathZ
|
|
||||||
\lthtmlcheckvsize\clearpage}
|
|
||||||
|
|
||||||
{\newpage\clearpage
|
|
||||||
% contents=$r \in W$
|
|
||||||
\lthtmlinlinemathA{tex2html_wrap_inline804}%
|
|
||||||
$r \in W$%
|
|
||||||
\lthtmlinlinemathZ
|
|
||||||
\lthtmlcheckvsize\clearpage}
|
|
||||||
|
|
||||||
{\newpage\clearpage
|
|
||||||
% contents=begin{displaymath} N_r = \left\{s \in W: |a_{rs}| > \theta \sqrt{|a_{rr}a_{ss}|} \right\} \cup \left\{ r \right\} , end{displaymath}
|
|
||||||
\lthtmldisplayA{displaymath576}%
|
|
||||||
\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
|
|
||||||
% contents=$\theta \in [0,1]$
|
|
||||||
\lthtmlinlinemathA{tex2html_wrap_inline806}%
|
|
||||||
$\theta \in [0,1]$%
|
|
||||||
\lthtmlinlinemathZ
|
|
||||||
\lthtmlcheckvsize\clearpage}
|
|
||||||
|
|
||||||
{\newpage\clearpage
|
|
||||||
% contents=$i$
|
|
||||||
\lthtmlinlinemathA{tex2html_wrap_inline808}%
|
|
||||||
$i$%
|
|
||||||
\lthtmlinlinemathZ
|
|
||||||
\lthtmlcheckvsize\clearpage}
|
|
||||||
|
|
||||||
{\newpage\clearpage
|
|
||||||
% contents=$W_i^0$
|
|
||||||
\lthtmlinlinemathA{tex2html_wrap_inline810}%
|
|
||||||
$W_i^0$%
|
|
||||||
\lthtmlinlinemathZ
|
|
||||||
\lthtmlcheckvsize\clearpage}
|
|
||||||
|
|
||||||
{\newpage\clearpage
|
|
||||||
% contents=$P_C=R_C^T$
|
|
||||||
\lthtmlinlinemathA{tex2html_wrap_inline814}%
|
|
||||||
$P_C=R_C^T$%
|
|
||||||
\lthtmlinlinemathZ
|
|
||||||
\lthtmlcheckvsize\clearpage}
|
|
||||||
|
|
||||||
{\newpage\clearpage
|
|
||||||
% contents=$P \in \Re^{n \times n_C}$
|
|
||||||
\lthtmlinlinemathA{tex2html_wrap_inline816}%
|
|
||||||
$P \in \Re^{n \times n_C}$%
|
|
||||||
\lthtmlinlinemathZ
|
|
||||||
\lthtmlcheckvsize\clearpage}
|
|
||||||
|
|
||||||
{\newpage\clearpage
|
|
||||||
% contents=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}
|
|
||||||
\lthtmldisplayA{displaymath533}%
|
|
||||||
\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
|
|
||||||
% contents=$P_C$
|
|
||||||
\lthtmlinlinemathA{tex2html_wrap_inline818}%
|
|
||||||
$P_C$%
|
|
||||||
\lthtmlinlinemathZ
|
|
||||||
\lthtmlcheckvsize\clearpage}
|
|
||||||
|
|
||||||
{\newpage\clearpage
|
|
||||||
% contents=$P$
|
|
||||||
\lthtmlinlinemathA{tex2html_wrap_inline820}%
|
|
||||||
$P$%
|
|
||||||
\lthtmlinlinemathZ
|
|
||||||
\lthtmlcheckvsize\clearpage}
|
|
||||||
|
|
||||||
{\newpage\clearpage
|
|
||||||
% contents=$S \in \Re^{n \times n}$
|
|
||||||
\lthtmlinlinemathA{tex2html_wrap_inline822}%
|
|
||||||
$S \in \Re^{n \times n}$%
|
|
||||||
\lthtmlinlinemathZ
|
|
||||||
\lthtmlcheckvsize\clearpage}
|
|
||||||
|
|
||||||
{\newpage\clearpage
|
|
||||||
% contents=begin{displaymath} P_C = S P, end{displaymath}
|
|
||||||
\lthtmldisplayA{displaymath544}%
|
|
||||||
\begin{displaymath}
|
|
||||||
P_C = S P,
|
|
||||||
\end{displaymath}%
|
|
||||||
\lthtmldisplayZ
|
|
||||||
\lthtmlcheckvsize\clearpage}
|
|
||||||
|
|
||||||
{\newpage\clearpage
|
|
||||||
% contents=$S$
|
|
||||||
\lthtmlinlinemathA{tex2html_wrap_inline824}%
|
|
||||||
$S$%
|
|
||||||
\lthtmlinlinemathZ
|
|
||||||
\lthtmlcheckvsize\clearpage}
|
|
||||||
|
|
||||||
{\newpage\clearpage
|
|
||||||
% contents=begin{displaymath} S = I - \omega D^{-1} A , end{displaymath}
|
|
||||||
\lthtmldisplayA{displaymath548}%
|
|
||||||
\begin{displaymath}
|
|
||||||
S = I - \omega D^{-1} A ,
|
|
||||||
\end{displaymath}%
|
|
||||||
\lthtmldisplayZ
|
|
||||||
\lthtmlcheckvsize\clearpage}
|
|
||||||
|
|
||||||
{\newpage\clearpage
|
|
||||||
% contents=$\omega$
|
|
||||||
\lthtmlinlinemathA{tex2html_wrap_inline826}%
|
|
||||||
$\omega$%
|
|
||||||
\lthtmlinlinemathZ
|
|
||||||
\lthtmlcheckvsize\clearpage}
|
|
||||||
|
|
||||||
{\newpage\clearpage
|
|
||||||
% contents=$D^{-1}A$
|
|
||||||
\lthtmlinlinemathA{tex2html_wrap_inline828}%
|
|
||||||
$D^{-1}A$%
|
|
||||||
\lthtmlinlinemathZ
|
|
||||||
\lthtmlcheckvsize\clearpage}
|
|
||||||
|
|
||||||
\stepcounter{section}
|
|
||||||
{\newpage\clearpage
|
|
||||||
% contents=$\theta = 0$
|
|
||||||
\lthtmlinlinemathA{tex2html_wrap_inline985}%
|
|
||||||
$\theta = 0$%
|
|
||||||
\lthtmlinlinemathZ
|
|
||||||
\lthtmlcheckvsize\clearpage}
|
|
||||||
|
|
||||||
\stepcounter{subsection}
|
|
||||||
\stepcounter{section}
|
|
||||||
{\newpage\clearpage
|
|
||||||
% contents=$w$
|
|
||||||
\lthtmlinlinemathA{tex2html_wrap_inline1316}%
|
|
||||||
$w$%
|
|
||||||
\lthtmlinlinemathZ
|
|
||||||
\lthtmlcheckvsize\clearpage}
|
|
||||||
|
|
||||||
\stepcounter{subsection}
|
|
||||||
\stepcounter{subsection}
|
|
||||||
{\newpage\clearpage
|
|
||||||
% contents=$\ge 0$
|
|
||||||
\lthtmlinlinemathA{tex2html_wrap_inline1320}%
|
|
||||||
$\ge 0$%
|
|
||||||
\lthtmlinlinemathZ
|
|
||||||
\lthtmlcheckvsize\clearpage}
|
|
||||||
|
|
||||||
{\newpage\clearpage
|
|
||||||
% contents=$t$
|
|
||||||
\lthtmlinlinemathA{tex2html_wrap_inline1334}%
|
|
||||||
$t$%
|
|
||||||
\lthtmlinlinemathZ
|
|
||||||
\lthtmlcheckvsize\clearpage}
|
|
||||||
|
|
||||||
{\newpage\clearpage
|
|
||||||
% contents=$\in [0, 1]$
|
|
||||||
\lthtmlinlinemathA{tex2html_wrap_inline1338}%
|
|
||||||
$\in [0, 1]$%
|
|
||||||
\lthtmlinlinemathZ
|
|
||||||
\lthtmlcheckvsize\clearpage}
|
|
||||||
|
|
||||||
{\newpage\clearpage
|
|
||||||
% contents=$\theta$
|
|
||||||
\lthtmlinlinemathA{tex2html_wrap_inline1340}%
|
|
||||||
$\theta$%
|
|
||||||
\lthtmlinlinemathZ
|
|
||||||
\lthtmlcheckvsize\clearpage}
|
|
||||||
|
|
||||||
{\newpage\clearpage
|
|
||||||
% contents=$4/(3||D^{-1}A||_\infty)$
|
|
||||||
\lthtmlinlinemathA{tex2html_wrap_inline1346}%
|
|
||||||
$4/(3||D^{-1}A||_\infty)$%
|
|
||||||
\lthtmlinlinemathZ
|
|
||||||
\lthtmlcheckvsize\clearpage}
|
|
||||||
|
|
||||||
{\newpage\clearpage
|
|
||||||
% contents=$> 0$
|
|
||||||
\lthtmlinlinemathA{tex2html_wrap_inline1362}%
|
|
||||||
$> 0$%
|
|
||||||
\lthtmlinlinemathZ
|
|
||||||
\lthtmlcheckvsize\clearpage}
|
|
||||||
|
|
||||||
\stepcounter{subsection}
|
|
||||||
\stepcounter{subsection}
|
|
||||||
{\newpage\clearpage
|
|
||||||
% contents=$y = op(M^{-1})\, x$
|
|
||||||
\lthtmlinlinemathA{tex2html_wrap_inline1374}%
|
|
||||||
$y = op(M^{-1})\, x$%
|
|
||||||
\lthtmlinlinemathZ
|
|
||||||
\lthtmlcheckvsize\clearpage}
|
|
||||||
|
|
||||||
{\newpage\clearpage
|
|
||||||
% contents=$op$
|
|
||||||
\lthtmlinlinemathA{tex2html_wrap_inline1378}%
|
|
||||||
$op$%
|
|
||||||
\lthtmlinlinemathZ
|
|
||||||
\lthtmlcheckvsize\clearpage}
|
|
||||||
|
|
||||||
{\newpage\clearpage
|
|
||||||
% contents=$x$
|
|
||||||
\lthtmlinlinemathA{tex2html_wrap_inline1382}%
|
|
||||||
$x$%
|
|
||||||
\lthtmlinlinemathZ
|
|
||||||
\lthtmlcheckvsize\clearpage}
|
|
||||||
|
|
||||||
{\newpage\clearpage
|
|
||||||
% contents=$y$
|
|
||||||
\lthtmlinlinemathA{tex2html_wrap_inline1384}%
|
|
||||||
$y$%
|
|
||||||
\lthtmlinlinemathZ
|
|
||||||
\lthtmlcheckvsize\clearpage}
|
|
||||||
|
|
||||||
{\newpage\clearpage
|
|
||||||
% contents=$op(M^{-1}) = M^{-1}$
|
|
||||||
\lthtmlinlinemathA{tex2html_wrap_inline1386}%
|
|
||||||
$op(M^{-1}) = M^{-1}$%
|
|
||||||
\lthtmlinlinemathZ
|
|
||||||
\lthtmlcheckvsize\clearpage}
|
|
||||||
|
|
||||||
{\newpage\clearpage
|
|
||||||
% contents=$op(M^{-1}) = M^{-T}$
|
|
||||||
\lthtmlinlinemathA{tex2html_wrap_inline1388}%
|
|
||||||
$op(M^{-1}) = M^{-T}$%
|
|
||||||
\lthtmlinlinemathZ
|
|
||||||
\lthtmlcheckvsize\clearpage}
|
|
||||||
|
|
||||||
{\newpage\clearpage
|
|
||||||
% contents=$M^{-1})$
|
|
||||||
\lthtmlinlinemathA{tex2html_wrap_inline1390}%
|
|
||||||
$M^{-1})$%
|
|
||||||
\lthtmlinlinemathZ
|
|
||||||
\lthtmlcheckvsize\clearpage}
|
|
||||||
|
|
||||||
{\newpage\clearpage
|
|
||||||
% contents=$op(M^{-1}) = M^{-C}$
|
|
||||||
\lthtmlinlinemathA{tex2html_wrap_inline1392}%
|
|
||||||
$op(M^{-1}) = M^{-C}$%
|
|
||||||
\lthtmlinlinemathZ
|
|
||||||
\lthtmlcheckvsize\clearpage}
|
|
||||||
|
|
||||||
\stepcounter{subsection}
|
|
||||||
\stepcounter{subsection}
|
|
||||||
\stepcounter{section}
|
|
||||||
\appendix
|
|
||||||
\stepcounter{section}
|
|
||||||
|
|
||||||
\end{document}
|
|
Loading…
Reference in New Issue