给我一个gmres求解线性方程组的matlab代码
时间: 2024-05-23 09:14:37 浏览: 125
以下是一个使用GMRES方法求解线性方程组Ax=b的Matlab代码示例:
function [x,flag,relres,iter,resvec] = gmres_solver(A,b,restart,max_iter,tol)
% input:
% A: 系数矩阵
% b: 右端向量
% restart: GMRES的重启参数
% max_iter: 最大迭代次数
% tol: 计算相对残差的误差容限
n = size(A,1);
x = zeros(n,1);
residual = b - A*x;
beta = norm(residual);
V(:,1) = residual / beta;
H = zeros(restart+1,restart);
flag = 0;
iter = 0;
resvec = [];
while(iter < max_iter && flag == 0)
iter = iter + 1;
for j = 1:restart
w = A*V(:,j);
for i = 1:j
H(i,j) = V(:,i)'*w;
w = w - H(i,j)*V(:,i);
end
H(j+1,j) = norm(w);
if H(j+1,j) ~= 0 && j < restart
V(:,j+1) = w / H(j+1,j);
end
for i = 1:j-1
H(i,j) = H(i,j) / H(j,j);
H(i+1:j,j) = H(i+1:j,j) - H(i,j)*H(i+1:j,j);
end
H(j+1,j) = norm( H(j+1:j,j) );
if H(j+1,j) ~= 0 && j < restart
V(:,j+1) = V(:,j+1) - V(:,1:j)*((V(:,1:j)'*V(:,j+1))\V(:,1:j)'*V(:,j+1));
end
y = H(1:j+1,1:j) \ [beta; zeros(j,1)];
x = x + V(:,1:j)*y;
residual = b - A*x;
resvec(iter) = norm(residual);
if resvec(iter) < tol
flag = 1;
break;
end
end
end
if flag == 1
relres = resvec(iter) / norm(b);
else
relres = resvec(end) / norm(b);
end
end
在使用时,您需要输入系数矩阵A和右端向量b,并设置GMRES的一些参数(如重启参数、最大迭代次数和误差容限)。然后,该函数将返回解向量x、收敛标志flag、相对残差relres、迭代次数iter和残差向量resvec。
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