cgnr.m

求解线性系统的Krylov方法的工具箱

%function [y,x]=CGNR(A,b,x0)
%developped by Plum
%this algorithm is to sovle the linear system Ax=b
%where A is a n-by-n matrix
function [y,x]=CGNR(A,b,x0)
k=0;
x0=zeros(length(A),1);
r=b-A*x0;x=x0;
err=1;p=A'*r;rr=p'*p;
while err>0.000001
    k=k+1;
    if k<100
        w=A*p;
        alpha=rr/(w'*w);
        x=x+alpha*p;
        r=r-alpha*w;
        err=norm(r,inf);
        z=A'*r;zz=z'*z;
        beta=zz/rr;rr=zz;
        p=z+beta*p;
    else
        break;
    end
end
y=k;