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


$key = q/displaystyle1slashs_j={frac{1}{j+1}}sum_{k=0}^jv_k^{2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="163" HEIGHT="72" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img5.png"
 ALT="$\displaystyle 1/ s_j = {\frac{1}{j+1}}\sum_{k=0}^j v_k^{2} .$">|; 

$key = q/displaystyleDeltav_k=v_ksum_{j=k}^infty[-2,s_j^2slash(j+1)]Deltas_j.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="263" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img10.png"
 ALT="$\displaystyle \Delta v_k = v_k \sum_{j=k}^\infty [-2   s_j^2 /(j+1)] \Delta s_j .$">|; 

$key = q/displaystyleleft{s_j-left[{frac{1}{j+1}}sum_{k=0}^j(stensor{B}cdotsvector{w})_k^2right]^{-1}right}^2+epsilonsum_k{w_k^2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="347" HEIGHT="93" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img14.png"
 ALT="$\displaystyle \left \{ s_j -
\left [ {\frac{1}{j+1}}\sum_{k=0}^j
( \stensor{B} \cdot \svector{w})_k^2
\right ]^{-1} \right \}^2
+ \epsilon \sum_k { w_k^2 } .$">|; 

$key = q/epsilon;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img15.png"
 ALT="$\epsilon$">|; 

$key = q/Deltasvector{s};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img16.png"
 ALT="$\Delta \svector{s}$">|; 

$key = q/Deltav_k;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img7.png"
 ALT="$\Delta v_k$">|; 

$key = q/Deltasvector{w};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img17.png"
 ALT="$\Delta \svector{w}$">|; 

$key = q/svector{w};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img13.png"
 ALT="$\svector{w}$">|; 

$key = q/b(r)=r^2(2r-3)+1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="176" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1.png"
 ALT="$b(r) = r^2 (2 r - 3) + 1$">|; 

$key = q/displaystylev_k=left(frac{k}{s_k}-frac{k-1}{s_{k-1}}right)^{frac{1}{2}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="183" HEIGHT="80" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img6.png"
 ALT="$\displaystyle v_k = \left ( \frac{k}{s_k} - \frac{k-1}{s_{k-1}} \right )^{\frac{1}{2}} .$">|; 

$key = q/rleq1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2.png"
 ALT="$r \leq 1$">|; 

$key = q/displaystyleleft[Deltas_j-frac{2s_j^2}{j+1}sum_{k=0}^j(stensor{B}cdotsvector{w})dotDeltasvector{w})_kright]^2+epsilonsum_k{(w_k+Deltaw_k)^2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="481" HEIGHT="82" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img18.png"
 ALT="$\displaystyle \left [ \Delta s_j -
\frac{2 s_j^2}{j+1} \sum_{k=0}^j
( \stenso...
... \Delta \svector{w})_k
\right ]^2
+ \epsilon \sum_k { (w_k + \Delta w_k) ^2 } .$">|; 

$key = q/svector{s};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img3.png"
 ALT="$\svector{s}$">|; 

$key = q/displaystyleDeltas_j=[-2,s_j^2slash(j+1)]sum_{k=0}^jv_kDeltav_k.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="267" HEIGHT="72" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img9.png"
 ALT="$\displaystyle \Delta s_j = [ -2   s_j^2 / (j+1) ] \sum_{k=0}^j v_k \Delta v_k .$">|; 

$key = q/svector{v};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img4.png"
 ALT="$\svector{v}$">|; 

$key = q/Deltas_j;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img8.png"
 ALT="$\Delta s_j$">|; 

$key = q/displaystylev_kequivsum_{i}b_{k-i},w_iequiv(stensor{B}cdotsvector{w})_k.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="225" HEIGHT="50" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img12.png"
 ALT="$\displaystyle v_k \equiv \sum_{i} b_{k-i}   w_i
\equiv (\stensor{B} \cdot \svector{w} )_k .$">|; 

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

1;