my_pcg_schur.m

求解线性系统的Krylov方法的工具箱

function [x,iter,flg]=my_pcg_schur(L,U,B,C,b,tol,maxit,x0)
% [x,iter,flg,operations]=my_pcg_schur(L,U,B,C,b,tol,maxit,M1,D,M2,x0)
% This code implements CG algorithm with preconditioners M1 and M2, D if
% necessary
% flg=0 success; flg=1 fail;

% Developed by: Plum_Liliang UESTC China
% Date        : 2006-05-13
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

[m,n] = size(B);
% if 'b' is zero then the solution is zero
norm_b=norm(b);
if norm_b==0
    x=0;
    iter=0;
    return;
end

% set up for the PCG method
x=x0;
r=b-schur_Ax(L,U,B,C,x);
rho=1;
flg=1;
iter=maxit;
for k=1:maxit
    z = r;    
    rho1=rho;
    rho=r'*z;
    % The search direction
    if k==1
        p=z;
    else
        beta=rho/rho1;
        p=r+beta*p;
    end
    % 
    w=schur_Ax(L,U,B,C,p);
    alpha=rho/(p'*w);
    x=x+alpha*p;
    r=r-alpha*w;
    norm_r=norm(r);
    if norm_r<tol
        flg=0;
        iter=k;
        break;
    end
end