给我一个预处理共轭梯度法求解线性方程组的matlab参考程序
时间: 2024-04-02 17:22:44 浏览: 11
以下是一个预处理共轭梯度法求解线性方程组的matlab参考程序:
%设置矩阵A,向量b和初始解x0
A = [4 -1 0 -1 0 0; -1 4 -1 0 -1 0; 0 -1 4 0 0 -1; -1 0 0 3 -1 -1; 0 -1 0 -1 3 -1; 0 0 -1 -1 -1 3];
b = [1; 0; 0; 0; 0; 0];
x0 = zeros(size(b));
%设置预处理矩阵M
D = diag(diag(A));
L = tril(A,-1);
U = triu(A,1);
M = inv(D)*(L+U);
%设置预处理向量z和搜索方向p
z0 = zeros(size(b));
z = z0;
p = z0;
%设置预处理迭代的容差tol和最大迭代次数maxit
tol = 1e-6;
maxit = 1000;
%预处理共轭梯度法迭代过程
r = b-A*x0;
z = M\r;
p = z;
for iter = 1:maxit
Ap = A*p;
alpha = (z'*r)/(p'*Ap);
x = x0 + alpha*p;
r = r - alpha*Ap;
if norm(r) < tol
break;
end
z = M\r;
beta = (z'*r)/(p'*Ap);
p = z + beta*p;
x0 = x;
end
%输出结果
disp(['预处理共轭梯度法迭代',num2str(iter),'次得到的解是:']);
disp(x);