?? numerical_analysis1.m
字號:
clear;n=1000;k=400;H=hilb(n);%Get A5----------------------------------------d0=diag(H);d1=diag(H,-1);d2=diag(H,1);d3=diag(H,-2);d4=diag(H,2);A3=diag(d0)+diag(d1,-1)+diag(d2,1);A5=diag(d0)+diag(d1,-1)+diag(d2,1)+diag(d3,-2)+diag(d4,2);xs=10.*rand(n,1);%[6.0854 0.1576 0.1635 1.9007 5.8692 0.5758 3.6757 6.3145 7.1763 6.9267 0.8408 4.5436 4.4183 3.5325].';%10.*rand(n,1);b=H*xs;tic%PCG Algorithms*********************************%initialization--------------------------------R=zeros(n,k+1);X=zeros(n,k+1);P=zeros(n,k+1);Z=zeros(n,k+1);alfa=zeros(1,k);beta=zeros(1,k);r=zeros(1,k+1);R(:,1)=b;P(:,1)=A5\b;Z(:,1)=P(:,1);r(1)=normest(b);%iteration-------------------------------------for j=1:k alfa(j)=( R(:,j).'*Z(:,j) )./( P(:,j).'*(H*P(:,j)) ); X(:,j+1)=X(:,j)+alfa(j).*P(:,j); R(:,j+1)=R(:,j)-alfa(j).*(H*P(:,j)); r(j+1)=normest(R(:,j+1)); if r(j+1)<=1e-7 break; end Z(:,j+1)=A5\R(:,j+1); beta(j)=( R(:,j+1).'*Z(:,j+1) )./( R(:,j).'*Z(:,j) ); P(:,j+1)=Z(:,j+1)+beta(j).*P(:,j);endx5=X(:,j+1);step5=jtoctic%PCG Algorithms*********************************%initialization--------------------------------R=zeros(n,k+1);X3=zeros(n,k+1);P=zeros(n,k+1);Z=zeros(n,k+1);alfa=zeros(1,k);beta=zeros(1,k);r=zeros(1,k+1);R(:,1)=b;P(:,1)=A3\b;Z(:,1)=P(:,1);r(1)=normest(b);%iteration-------------------------------------for j=1:k alfa(j)=( R(:,j).'*Z(:,j) )./( P(:,j).'*(H*P(:,j)) ); X3(:,j+1)=X3(:,j)+alfa(j).*P(:,j); R(:,j+1)=R(:,j)-alfa(j).*(H*P(:,j)); r(j+1)=normest(R(:,j+1)); if r(j+1)<=1e-7 break; end Z(:,j+1)=A3\R(:,j+1); beta(j)=( R(:,j+1).'*Z(:,j+1) )./( R(:,j).'*Z(:,j) ); P(:,j+1)=Z(:,j+1)+beta(j).*P(:,j);endx3=X3(:,j+1);step3=jtocdel3=delta(x3,xs)del5=delta(x5,xs)?? 快捷鍵說明
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