# LaTeX2HTML 0.6.4 (Tues Aug 30 1994)
# Associate image original text (scrambled) with physical files.
$key = q/{}$L_21^T${}/;
$cached_env_img{$key} ='
';
$key = q/{}$v_i${}/;
$cached_env_img{$key} ='
';
$key = q/{}$13,N^3${}/;
$cached_env_img{$key} ='
';
$key = q/{displaymath}GproptofracT_s(N)T_p(N,N_p)=N_p,E(N,N_p),{displaymath}/;
$cached_env_img{$key} ='
';
$key = q/{figure}centeringcenterlinehboxpsfigfigure=QR.psmedskiplabelfig:qrsnap{figure}/;
$cached_env_img{$key} ='
';
$key = q/{}$A_2=left(arraycA_12A_22arrayright)${}/;
$cached_env_img{$key} ='
';
$key = q/{}$A_22${}/;
$cached_env_img{$key} ='
';
$key = q/{}$V${}/;
$cached_env_img{$key} ='
';
$key = q/{figure}centeringcenterlinehboxhskip0.25inpsfigfigure=delta_llt_nb.psvskip0.2inlabelfig:figlltd{figure}/;
$cached_env_img{$key} ='
';
$key = q/{}$mlongmapstoleftlanglep,b,irightrangle${}/;
$cached_env_img{$key} ='
';
$key = q/{}$N=9600${}/;
$cached_env_img{$key} ='
';
$key = q/{}$T${}/;
$cached_env_img{$key} ='
';
$key = q/{}$A_12${}/;
$cached_env_img{$key} ='
';
$key = q/{}$2times3${}/;
$cached_env_img{$key} ='
';
$key = q/{}$(n-n_b)timesn_b${}/;
$cached_env_img{$key} ='
';
$key = q/{}$R${}/;
$cached_env_img{$key} ='
';
$key = q/{}$L_0${}/;
$cached_env_img{$key} ='
';
$key = q/{}$m_b=lceilMPrceil${}/;
$cached_env_img{$key} ='
';
$key = q/{}$6times4${}/;
$cached_env_img{$key} ='
';
$key = q/{}$P${}/;
$cached_env_img{$key} ='
';
$key = q/{}$n_bge6${}/;
$cached_env_img{$key} ='
';
$key = q/{}$PtimesQ${}/;
$cached_env_img{$key} ='
';
$key = q/{}$N${}/;
$cached_env_img{$key} ='
';
$key = q/{figure}centeringcenterlinehboxhskip0.25inpsfigfigure=comp_llt.psvskip0.2inlabelfig:figlltc{figure}/;
$cached_env_img{$key} ='
';
$key = q/{}$23,N^3${}/;
$cached_env_img{$key} ='
';
$key = q/{}$mtimes(n-n_b)${}/;
$cached_env_img{$key} ='
';
$key = q/{}$A_1=left(arraycA_11A_21arrayright)${}/;
$cached_env_img{$key} ='
';
$key = q/{}$A_2${}/;
$cached_env_img{$key} ='
';
$key = q/{}$tildeA_22${}/;
$cached_env_img{$key} ='
';
$key = q/{}$L${}/;
$cached_env_img{$key} ='
';
$key = q/{}$(N_p,G)${}/;
$cached_env_img{$key} ='
';
$key = q/{}$L_21${}/;
$cached_env_img{$key} ='
';
$key = q/{}$12leqPQleq1${}/;
$cached_env_img{$key} ='
';
$key = q/{}$WleftarrowV^TA_2${}/;
$cached_env_img{$key} ='
';
$key = q/{}$H_i=I-tau_iv_iv_i^T${}/;
$cached_env_img{$key} ='
';
$key = q/{}$A=PLU${}/;
$cached_env_img{$key} ='
';
$key = q/{}$A=LL^T${}/;
$cached_env_img{$key} ='
';
$key = q/{}$L_11${}/;
$cached_env_img{$key} ='
';
$key = q/{figure}centeringcenterlinehboxhskip0.25inpsfigfigure=comp_qr.psvskip0.2inlabelfig:figqrc{figure}/;
$cached_env_img{$key} ='
';
$key = q/{}$tildeA_22leftarrowA_22-L_21L_21^T=L_22L_22^T${}/;
$cached_env_img{$key} ='
';
$key = q/{}$tildeA_22leftarrowA_22-L_21U_12=L_22U_22.${}/;
$cached_env_img{$key} ='
';
$key = q/{}$N_p${}/;
$cached_env_img{$key} ='
';
$key = q/{}$n_b${}/;
$cached_env_img{$key} ='
';
$key = q/{}$(n_b-i)${}/;
$cached_env_img{$key} ='
';
$key = q/{}$m=M-(k-1)cdotn_b${}/;
$cached_env_img{$key} ='
';
$key = q/{}$L^(k)${}/;
$cached_env_img{$key} ='
';
$key = q/{}$16times16${}/;
$cached_env_img{$key} ='
';
$key = q/{}$L_21leftarrowA_21(L_11^T)^-1${}/;
$cached_env_img{$key} ='
';
$key = q/{}$43,N^3${}/;
$cached_env_img{$key} ='
';
$key = q/{}$(m,n)${}/;
$cached_env_img{$key} ='
';
$key = q/{}$R_11${}/;
$cached_env_img{$key} ='
';
$key = q/{}$L^(k)^T${}/;
$cached_env_img{$key} ='
';
$key = q/{}$m_btimesn_b${}/;
$cached_env_img{$key} ='
';
$key = q/{}$V_1${}/;
$cached_env_img{$key} ='
';
$key = q/{}$NtimesN${}/;
$cached_env_img{$key} ='
';
$key = q/{}$L^T_21${}/;
$cached_env_img{$key} ='
';
$key = q/{}$tau_i=2(v_i^Tv_i)${}/;
$cached_env_img{$key} ='
';
$key = q/{displaymath}mlongmapstoleftlangles,rmmod,P,,leftlfloorfracsPrightrfloor,,m,rmmod,m_brightrangle{displaymath}/;
$cached_env_img{$key} ='
';
$key = q/{displaymath}(m,n)longmapstoleftlangle(m,rmmod,P,,n,rmmod,Q),left(leftlfloorvphantomfracnQfracmPrightrfloor,leftlfloorfracnQrightrfloorright),,(0,0)rightrangle.{displaymath}/;
$cached_env_img{$key} ='
';
$key = q/{}$tau${}/;
$cached_env_img{$key} ='
';
$key = q/{}$tildeA_2leftarrowleft(arrayctildeR_12tildeR_22arrayright)=A_2-VW${}/;
$cached_env_img{$key} ='
';
$key = q/{}$m${}/;
$cached_env_img{$key} ='
';
$key = q/{}$A_:i${}/;
$cached_env_img{$key} ='
';
$key = q/{}$k${}/;
$cached_env_img{$key} ='
';
$key = q/{}$A_21${}/;
$cached_env_img{$key} ='
';
$key = q/{}$12times12${}/;
$cached_env_img{$key} ='
';
$key = q/{}$Q^TA=(I-VTV^T)A${}/;
$cached_env_img{$key} ='
';
$key = q/{}$0,1,cdots,M-1${}/;
$cached_env_img{$key} ='
';
$key = q/{}$i${}/;
$cached_env_img{$key} ='
';
$key = q/{}$mtimesn${}/;
$cached_env_img{$key} ='
';
$key = q/{}$m_b=n_b=1${}/;
$cached_env_img{$key} ='
';
$key = q/{}$A_11${}/;
$cached_env_img{$key} ='
';
$key = q/{figure}centeringcenterlinehboxpsfigfigure=cyclic.pssmallskiplabelfig:mview{figure}/;
$cached_env_img{$key} ='
';
$key = q/{}$n_b=lceilNQrceil${}/;
$cached_env_img{$key} ='
';
$key = q/{}$P_i${}/;
$cached_env_img{$key} ='
';
$key = q/{}dag{}/;
$cached_env_img{$key} ='
';
$key = q/{}$k=1,2,cdots${}/;
$cached_env_img{$key} ='
';
$key = q/{figure}centeringcenterlinehboxpsfigfigure=qrv.pslabelfig:qrvstore{figure}/;
$cached_env_img{$key} ='
';
$key = q/{}$A^(k)${}/;
$cached_env_img{$key} ='
';
$key = q/{}$V_2${}/;
$cached_env_img{$key} ='
';
$key = q/{}$U_12${}/;
$cached_env_img{$key} ='
';
$key = q/{}$Q=H_1H_2cdotsH_n_b=I-VTV^T${}/;
$cached_env_img{$key} ='
';
$key = q/{}$W${}/;
$cached_env_img{$key} ='
';
$key = q/{displaymath}(m,n)longmapstoleftlangleleft(leftlfloorfracmm_brightrfloor,leftlfloorfracnn_brightrfloorright),,(0,0),,(m,rmmod,m_b,n,rmmod,n_b)rightrangle.{displaymath}/;
$cached_env_img{$key} ='
';
$key = q/{}$U${}/;
$cached_env_img{$key} ='
';
$key = q/{}$tildeA_1leftarrowH_i^TA_1=(I-tau_iv_iv_i^T)A_1${}/;
$cached_env_img{$key} ='
';
$key = q/{}$tildeA_2leftarrowleft(arrayctildeR_12tildeR_22arrayright)=Q^TA_2=left(I-VT^TV^Tright)A_2${}/;
$cached_env_img{$key} ='
';
$key = q/{}$Q${}/;
$cached_env_img{$key} ='
';
$key = q/{}$N=10000${}/;
$cached_env_img{$key} ='
';
$key = q/{}$MtimesM${}/;
$cached_env_img{$key} ='
';
$key = q/{}$WleftarrowT^TW${}/;
$cached_env_img{$key} ='
';
$key = q/{}$14leqPQleq12${}/;
$cached_env_img{$key} ='
';
$key = q/{}$(m-n_b)times(n-n_b)${}/;
$cached_env_img{$key} ='
';
$key = q/{}$M${}/;
$cached_env_img{$key} ='
';
$key = q/{displaymath}A^(k)=left(arrayccA_1;html_special_mark_amp;A_2arrayright)=left(arrayccA_11;html_special_mark_amp;A_12A_21;html_special_mark_amp;A_22arrayright)=Qcdotleft(arrayccR_11;html_special_mark_amp;R_120;html_special_mark_amp;R_22arrayright){displaymath}/;
$cached_env_img{$key} ='
';
$key = q/{figure}centeringcenterlinehboxhskip0.25inpsfigfigure=pgon_ft_sca.psvskip0.2inlabelfig:figpgonb{figure}/;
$cached_env_img{$key} ='
';
$key = q/{}$G${}/;
$cached_env_img{$key} ='
';
$key = q/{}$8times16${}/;
$cached_env_img{$key} ='
';
$key = q/{}$E${}/;
$cached_env_img{$key} ='
';
$key = q/{}$i=1,cdots,n_b${}/;
$cached_env_img{$key} ='
';
$key = q/{}$N=26000${}/;
$cached_env_img{$key} ='
';
$key = q/{}$A${}/;
$cached_env_img{$key} ='
';
$key = q/{}$n=N-(k-1)cdotn_b${}/;
$cached_env_img{$key} ='
';
$key = q/{}$(n-n_b)${}/;
$cached_env_img{$key} ='
';
$key = q/{displaymath}(m,n)longmapstoleftlangle(p,q),(b,d),(i,j)rightrangle.{displaymath}/;
$cached_env_img{$key} ='
';
$key = q/{}$mtimesn_b${}/;
$cached_env_img{$key} ='
';
$key = q/{}$m_b=n_b=8${}/;
$cached_env_img{$key} ='
';
$key = q/{figure}centeringcenterlinehboxpsfigfigure=LLT.psmedskiplabelfig:lltsnap{figure}/;
$cached_env_img{$key} ='
';
$key = q/{}$T_p(N,N_p)${}/;
$cached_env_img{$key} ='
';
$key = q/{}$A_11rightarrowL_11L_11^T${}/;
$cached_env_img{$key} ='
';
$key = q/{figure}centeringcenterlinehboxhskip0.25inpsfigfigure=comp_lu.psvskip0.2inlabelfig:figluc{figure}/;
$cached_env_img{$key} ='
';
$key = q/{}$barV${}/;
$cached_env_img{$key} ='
';
$key = q/{figure}centeringcenterlinehboxpsfigfigure=blocks.pssmallskiplabelfig:scalaview{figure}/;
$cached_env_img{$key} ='
';
$key = q/{}$s=lfloormm_brfloor${}/;
$cached_env_img{$key} ='
';
$key = q/{}$A=QR${}/;
$cached_env_img{$key} ='
';
$key = q/{}$N=36000${}/;
$cached_env_img{$key} ='
';
$key = q/{}$m_b=n_b=6${}/;
$cached_env_img{$key} ='
';
$key = q/{displaymath}tildeA_2=left(arrayctildeA_12tildeA_22arrayright)leftarrowleft(arraycR_12R_22arrayright)=Q^TA_2=left(I-VT^TV^Tright)A_2.{displaymath}/;
$cached_env_img{$key} ='
';
$key = q/{displaymath}V=left(arraycV_1V_2arrayright){displaymath}/;
$cached_env_img{$key} ='
';
$key = q/{}$L_22${}/;
$cached_env_img{$key} ='
';
$key = q/{}$m_b=n_b${}/;
$cached_env_img{$key} ='
';
$key = q/{}$ntimesn${}/;
$cached_env_img{$key} ='
';
$key = q/{}$Q^T${}/;
$cached_env_img{$key} ='
';
$key = q/{}$p${}/;
$cached_env_img{$key} ='
';
$key = q/{figure}centeringcenterlinehboxpsfigfigure=LU.psmedskiplabelfig:lusnap{figure}/;
$cached_env_img{$key} ='
';
$key = q/{}$U_11${}/;
$cached_env_img{$key} ='
';
$key = q/{}$n_btimesn_b${}/;
$cached_env_img{$key} ='
';
$key = q/{}$i-1${}/;
$cached_env_img{$key} ='
';
$key = q/{}$(m-n_b)timesn_b${}/;
$cached_env_img{$key} ='
';
$key = q/{}$MtimesN${}/;
$cached_env_img{$key} ='
';
$key = q/{displaymath}E(N,N_p)=frac1N_pfracT_s(N)T_p(N,N_p){displaymath}/;
$cached_env_img{$key} ='
';
$key = q/{}$m_b${}/;
$cached_env_img{$key} ='
';
$key = q/{}$(n-n_b)times(n-n_b)${}/;
$cached_env_img{$key} ='
';
$key = q/{}$n_btimes(n-n_b)${}/;
$cached_env_img{$key} ='
';
$key = q/{}$U_12leftarrow(L_11)^-1A_12.${}/;
$cached_env_img{$key} ='
';
$key = q/{}$rmmin(M,N)${}/;
$cached_env_img{$key} ='
';
$key = q/{}$A_1${}/;
$cached_env_img{$key} ='
';
$key = q/{}$tau_i${}/;
$cached_env_img{$key} ='
';
$key = q/{}$b${}/;
$cached_env_img{$key} ='
';
$key = q/{}$A=U^TU${}/;
$cached_env_img{$key} ='
';
$key = q/{}$T_s(N)${}/;
$cached_env_img{$key} ='
';
$key = q/{}$R_12${}/;
$cached_env_img{$key} ='
';
$key = q/{}$n_b=24${}/;
$cached_env_img{$key} ='
';
1;