jacobiMATLAB代码

以下是 Jacobi 迭代的 MATLAB 代码示例：

function [x, iter] = jacobi(A, b, x0, tol, maxiter)
% Jacobi iteration method to solve linear system Ax = b
% Input:
%   A: coefficient matrix
%   b: right-hand side vector
%   x0: initial guess
%   tol: tolerance for stopping criterion
%   maxiter: maximum number of iterations
% Output:
%   x: solution vector
%   iter: number of iterations

% matrix size
n = size(A, 1);

% initialize solution vector and iteration counter
x = x0;
iter = 0;

% loop until convergence or maximum iterations reached
while norm(A*x - b) > tol && iter < maxiter
    % update solution vector
    for i = 1:n
        x(i) = (b(i) - A(i,[1:i-1 i+1:n]) * x([1:i-1 i+1:n])) / A(i,i);
    end
    % increment iteration counter
    iter = iter + 1;
end

% check if maximum iterations reached
if iter == maxiter
    warning('Maximum number of iterations reached');
end

其中，`A` 是系数矩阵，`b` 是右侧向量，`x0` 是初始猜测，`tol` 是停止标准的容差，`maxiter` 是允许的最大迭代次数。函数返回解向量 `x` 和迭代次数 `iter`。