jacobi迭代matlab代码
时间: 2023-07-09 18:50:14 浏览: 64
以下是Jacobi迭代的MATLAB代码示例:
```matlab
function [x, iter] = jacobi(A, b, x0, tol, maxiter)
% Jacobi iteration method for solving linear systems
% A: coefficient matrix
% b: right-hand side vector
% x0: initial guess vector
% tol: tolerance
% maxiter: maximum number of iterations
% x: solution vector
% iter: number of iterations
% Initialize
n = size(A,1);
x = x0;
iter = 0;
% Perform iterations
while iter < maxiter
x_prev = x;
for i = 1:n
sigma = 0;
for j = 1:n
if j ~= i
sigma = sigma + A(i,j)*x(j);
end
end
x(i) = (b(i) - sigma)/A(i,i);
end
% Check for convergence
if norm(x - x_prev) < tol
break;
end
iter = iter + 1;
end
end
```
其中,A是系数矩阵,b是右侧向量,x0是初始猜测向量,tol是所需的精度,maxiter是最大迭代次数。循环中,迭代通过计算每个方程的当前猜测值和其他未知量的乘积之和,然后将其除以该方程系数来更新当前猜测值。如果新猜测与上一猜测之间的差小于所需精度,则迭代停止。函数返回解向量x和迭代次数iter。