# LaTeX2HTML 2008 (1.71)
# Associate images original text with physical files.


$key = q/{displaymath}min_{svector{scriptstylem}'}~~J_1(stensor{S}cdotsvector{m}')=J_2(sv(stensor{S}cdotsvector{m}')|^2+c|svector{m}'|^2.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="449" HEIGHT="41" BORDER="0"
 SRC="|."$dir".q|img21.png"
 ALT="\begin{displaymath}
\min_{\svector{\scriptstyle m}'}&nbsp;&nbsp;
J_1 ( \stensor{S} \cdot ...
... \cdot \svector{m}') \Vert^2
+ c \Vert \svector{m}' \Vert^2 .
\end{displaymath}">|; 

$key = q/svector{m}=stensor{S}cdotsvector{m}';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="96" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img20.png"
 ALT="$\svector{m} = \stensor{S} \cdot \svector{m}'$">|; 

$key = q/svector{f}(svector{m});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2.png"
 ALT="$\svector{f}( \svector{m})$">|; 

$key = q/forallsvector{m}_i';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img28.png"
 ALT="$\forall \svector{m}_i'$">|; 

$key = q/displaystylesvector{nabla}svector{f}(svector{m}_0)^*cdot[svector{d}-svector{f}(svector{m}_0)];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="187" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img12.png"
 ALT="$\displaystyle \svector{\nabla} \svector{f} ( \svector{m}_0 )^*
\cdot [ \svector{d} - \svector{f}( \svector{m}_0 ) ]$">|; 

$key = q/l^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="22" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img7.png"
 ALT="$l^2$">|; 

$key = q/textstyle=;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img11.png"
 ALT="$\textstyle =$">|; 

$key = q/svector{m};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img3.png"
 ALT="$\svector{m}$">|; 

$key = q/stensor{S_i};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img26.png"
 ALT="$\stensor{S_i}$">|; 

$key = q/displaystylestensor{S}^*cdotsvector{nabla}svector{f}(stensor{S}cdotsvector{m}'_0)^*cdot[svector{d}-svector{f}(stensor{S}cdotsvector{m}'_0)];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="272" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img23.png"
 ALT="$\displaystyle \stensor{S}^* \cdot
\svector{\nabla} \svector{f}
( \stensor{S} \...
...'_0 )^*
\cdot [ \svector{d} - \svector{f}( \stensor{S} \cdot \svector{m}'_0 ) ]$">|; 

$key = q/{displaymath}min_{svector{scriptstylem}}~~J_1(svector{m})=|svector{d}-svector{f}(svector{m})|^2+c|stensor{D}cdotsvector{m}|^2.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="335" HEIGHT="39" BORDER="0"
 SRC="|."$dir".q|img6.png"
 ALT="\begin{displaymath}
\min_{\svector{\scriptstyle m}}&nbsp;&nbsp;
J_1 (\svector{m} )=
\Vert...
...m}) \Vert^2
+ c \Vert \stensor{D} \cdot \svector{m} \Vert^2 .
\end{displaymath}">|; 

$key = q/i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img27.png"
 ALT="$i$">|; 

$key = q/svector{d};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="20" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1.png"
 ALT="$\svector{d}$">|; 

$key = q/svector{m}_{i+1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img32.png"
 ALT="$\svector{m}_{i+1}$">|; 

$key = q/svector{m}_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img31.png"
 ALT="$\svector{m}_i$">|; 

$key = q/stensor{S};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img16.png"
 ALT="$\stensor{S}$">|; 

$key = q/svector{m}';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img19.png"
 ALT="$\svector{m}'$">|; 

$key = q/j>i,strutexists~svector{m}_j'nistensor{S_j}cdotsvector{m}_j'=stensor{S_i}cdotsvector{m}_i';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="254" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img29.png"
 ALT="$j&gt;i, \strut \exists&nbsp; \svector{m}_j' \ni \stensor{S_j} \cdot \svector{m}_j'
= \stensor{S_i} \cdot \svector{m}_i'$">|; 

$key = q/textstyle+;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img13.png"
 ALT="$\textstyle +$">|; 

$key = q/{svector{m}_i=stensor{S_i}cdotsvector{m}'_i};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="127" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img30.png"
 ALT="$\{ \svector{m}_i = \stensor{S_i} \cdot \svector{m}'_i \}$">|; 

$key = q/c;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img9.png"
 ALT="$c$">|; 

$key = q/displaystylecsvector{m}'_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img24.png"
 ALT="$\displaystyle c \svector{m}'_0$">|; 

$key = q/stensor{S}^*;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img25.png"
 ALT="$\stensor{S}^*$">|; 

$key = q/stensor{D}cdotstensor{S}approxstensor{I};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="81" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img17.png"
 ALT="$\stensor{D} \cdot \stensor{S} \approx \stensor{I}$">|; 

$key = q/stensor{D};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4.png"
 ALT="$\stensor{D}$">|; 

$key = q/displaystylesvector{nabla}_{svector{scriptstylem}}J_1(svector{m}_0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="95" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img10.png"
 ALT="$\displaystyle \svector{\nabla}_{\svector{\scriptstyle m}} J_1 (\svector{m}_0 )$">|; 

$key = q/stensor{D}cdotsvector{m};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img5.png"
 ALT="$\stensor{D} \cdot \svector{m}$">|; 

$key = q/svector{m}_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img15.png"
 ALT="$\svector{m}_0$">|; 

$key = q/displaystylecstensor{D}^*cdotstensor{D}cdotsvector{m}_0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="112" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img14.png"
 ALT="$\displaystyle c \stensor{D}^* \cdot \stensor{D} \cdot \svector{m}_0 .$">|; 

$key = q/displaystylesvector{nabla}_{svector{scriptstylem}'}J_2(svector{m}'_0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="99" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img22.png"
 ALT="$\displaystyle \svector{\nabla}_{\svector{\scriptstyle m}'} J_2 (\svector{m}'_0 )$">|; 

$key = q/{displaymath}stensor{C}_m^{-1}equivE(svector{m}svector{m}^*)^{-1}=stensor{D}^*cdotstensor{D}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="232" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img8.png"
 ALT="\begin{displaymath}
\stensor{C}_m^{-1} \equiv E(\svector{m} \svector{m}^* )^{-1}
= \stensor{D}^* \cdot \stensor{D} .
\end{displaymath}">|; 

$key = q/{displaymath}stensor{C}_mequivE(svector{m}svector{m}^*)=stensor{S}^*cdotstensor{S}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="200" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img18.png"
 ALT="\begin{displaymath}
\stensor{C}_m \equiv E(\svector{m} \svector{m}^* )
= \stensor{S}^* \cdot \stensor{S} .
\end{displaymath}">|; 

1;