# LaTeX2HTML 2019.2 (Released June 5, 2019)
# Associate images original text with physical files.


$key = q/c;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.19ex; vertical-align: -0.10ex; " SRC="|."$dir".q|img9.svg"
 ALT="$c$">|; 

$key = q/displaystylecstensor{D}^*cdotstensor{D}cdotsvector{m}_0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.34ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img14.svg"
 ALT="$\displaystyle c \stensor{D}^* \cdot \stensor{D} \cdot \svector{m}_0 .$">|; 

$key = q/displaystylecsvector{m}'_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.58ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img24.svg"
 ALT="$\displaystyle c \svector{m}'_0$">|; 

$key = q/displaystylemin_{svector{scriptstylem}'}~~J_1(stensor{S}cdotsvector{m}')=J_2(sved}-svector{f}(stensor{S}cdotsvector{m}')|^2+c|svector{m}'|^2.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 3.74ex; vertical-align: -1.70ex; " SRC="|."$dir".q|img21.svg"
 ALT="$\displaystyle
\min_{\svector{\scriptstyle m}'}&nbsp;&nbsp;
J_1 ( \stensor{S} \cdot \svec...
...r{f}(\stensor{S} \cdot \svector{m}') \Vert^2
+ c \Vert \svector{m}' \Vert^2 .
$">|; 

$key = q/displaystylemin_{svector{scriptstylem}}~~J_1(svector{m})=|svector{d}-svector{f}(svector{m})|^2+c|stensor{D}cdotsvector{m}|^2.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 3.49ex; vertical-align: -1.45ex; " SRC="|."$dir".q|img6.svg"
 ALT="$\displaystyle
\min_{\svector{\scriptstyle m}}&nbsp;&nbsp;
J_1 (\svector{m} )=
\Vert \sve...
...tor{f}(\svector{m}) \Vert^2
+ c \Vert \stensor{D} \cdot \svector{m} \Vert^2 .
$">|; 

$key = q/displaystylestensor{C}_m^{-1}equivE(svector{m}svector{m}^*)^{-1}=stensor{D}^*cdotstensor{D}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.74ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img8.svg"
 ALT="$\displaystyle
\stensor{C}_m^{-1} \equiv E(\svector{m} \svector{m}^* )^{-1}
= \stensor{D}^* \cdot \stensor{D} .
$">|; 

$key = q/displaystylestensor{C}_mequivE(svector{m}svector{m}^*)=stensor{S}^*cdotstensor{S}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img18.svg"
 ALT="$\displaystyle
\stensor{C}_m \equiv E(\svector{m} \svector{m}^* )
= \stensor{S}^* \cdot \stensor{S} .
$">|; 

$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 STYLE="height: 2.58ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img23.svg"
 ALT="$\displaystyle \stensor{S}^* \cdot
\svector{\nabla} \svector{f}
( \stensor{S} \c...
...'_0 )^*
\cdot [ \svector{d} - \svector{f}( \stensor{S} \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 STYLE="height: 2.58ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img22.svg"
 ALT="$\displaystyle \svector{\nabla}_{\svector{\scriptstyle m}'} J_2 (\svector{m}'_0 )$">|; 

$key = q/displaystylesvector{nabla}_{svector{scriptstylem}}J_1(svector{m}_0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img10.svg"
 ALT="$\displaystyle \svector{\nabla}_{\svector{\scriptstyle m}} J_1 (\svector{m}_0 )$">|; 

$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 STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img12.svg"
 ALT="$\displaystyle \svector{\nabla} \svector{f} ( \svector{m}_0 )^*
\cdot [ \svector{d} - \svector{f}( \svector{m}_0 ) ]$">|; 

$key = q/forallsvector{m}_i';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.46ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img28.svg"
 ALT="$\forall \svector{m}_i'$">|; 

$key = q/i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.71ex; vertical-align: -0.10ex; " SRC="|."$dir".q|img27.svg"
 ALT="$i$">|; 

$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 STYLE="height: 3.25ex; vertical-align: -1.20ex; " SRC="|."$dir".q|img29.svg"
 ALT="$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/l^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.03ex; vertical-align: -0.10ex; " SRC="|."$dir".q|img7.svg"
 ALT="$l^2$">|; 

$key = q/stensor{D};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.23ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4.svg"
 ALT="$\stensor{D}$">|; 

$key = q/stensor{D}cdotstensor{S}approxstensor{I};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.23ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img17.svg"
 ALT="$\stensor{D} \cdot \stensor{S} \approx \stensor{I}$">|; 

$key = q/stensor{D}cdotsvector{m};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.23ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img5.svg"
 ALT="$\stensor{D} \cdot \svector{m}$">|; 

$key = q/stensor{S_i};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.58ex; vertical-align: -0.90ex; " SRC="|."$dir".q|img26.svg"
 ALT="$\stensor{S_i}$">|; 

$key = q/stensor{S};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.23ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img16.svg"
 ALT="$\stensor{S}$">|; 

$key = q/stensor{S}^*;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.34ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img25.svg"
 ALT="$\stensor{S}^*$">|; 

$key = q/svector{d};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.80ex; vertical-align: -0.10ex; " SRC="|."$dir".q|img1.svg"
 ALT="$\svector{d}$">|; 

$key = q/svector{f}(svector{m});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img2.svg"
 ALT="$\svector{f}( \svector{m})$">|; 

$key = q/svector{m}';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.89ex; vertical-align: -0.10ex; " SRC="|."$dir".q|img19.svg"
 ALT="$\svector{m}'$">|; 

$key = q/svector{m};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.22ex; vertical-align: -0.10ex; " SRC="|."$dir".q|img3.svg"
 ALT="$\svector{m}$">|; 

$key = q/svector{m}=stensor{S}cdotsvector{m}';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.34ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img20.svg"
 ALT="$\svector{m} = \stensor{S} \cdot \svector{m}'$">|; 

$key = q/svector{m}_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.57ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img15.svg"
 ALT="$\svector{m}_0$">|; 

$key = q/svector{m}_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.57ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img31.svg"
 ALT="$\svector{m}_i$">|; 

$key = q/svector{m}_{i+1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.73ex; vertical-align: -0.61ex; " SRC="|."$dir".q|img32.svg"
 ALT="$\svector{m}_{i+1}$">|; 

$key = q/textstyle+;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.70ex; vertical-align: -0.27ex; " SRC="|."$dir".q|img13.svg"
 ALT="$\textstyle +$">|; 

$key = q/textstyle=;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.03ex; vertical-align: -0.10ex; " SRC="|."$dir".q|img11.svg"
 ALT="$\textstyle =$">|; 

$key = q/{svector{m}_i=stensor{S_i}cdotsvector{m}'_i};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.72ex; vertical-align: -0.90ex; " SRC="|."$dir".q|img30.svg"
 ALT="$\{ \svector{m}_i = \stensor{S_i} \cdot \svector{m}'_i \}$">|; 

1;

