编写Jacobi迭代法、Gauss-Seidel迭代法和SOR迭代法的M文件

下面是Jacobi迭代法、Gauss-Seidel迭代法和SOR迭代法的MATLAB代码示例：

1. Jacobi迭代法 (jacobi.m):

function [x, iter] = jacobi(A, b, x0, tol, max_iter)
    n = size(A, 1);
    x = x0;
    iter = 0;
    
    while iter < max_iter
        x_new = zeros(n, 1);
        
        for i = 1:n
            x_new(i) = (b(i) - A(i, [1:i-1, i+1:n]) * x([1:i-1, i+1:n])) / A(i, i);
        end
        
        if norm(x_new - x) < tol
            break;
        end
        
        x = x_new;
        iter = iter + 1;
    end
    
    if iter == max_iter
        disp("Jacobi迭代法未收敛！");
    end
end

2. Gauss-Seidel迭代法 (gauss_seidel.m):

function [x, iter] = gauss_seidel(A, b, x0, tol, max_iter)
    n = size(A, 1);
    x = x0;
    iter = 0;
    
    while iter < max_iter
        x_new = zeros(n, 1);
        
        for i = 1:n
            x_new(i) = (b(i) - A(i, 1:i-1) * x_new(1:i-1) - A(i, i+1:n) * x(i+1:n)) / A(i, i);
        end
        
        if norm(x_new - x) < tol
            break;
        end
        
        x = x_new;
        iter = iter + 1;
    end
    
    if iter == max_iter
        disp("Gauss-Seidel迭代法未收敛！");
    end
end

3. SOR迭代法 (sor.m):

function [x, iter] = sor(A, b, x0, w, tol, max_iter)
    n = size(A, 1);
    x = x0;
    iter = 0;
    
    while iter < max_iter
        x_new = zeros(n, 1);
        
        for i = 1:n
            x_new(i) = (1 - w) * x(i) + (w / A(i, i)) * (b(i) - A(i, [1:i-1, i+1:n]) * x_new([1:i-1, i+1:n]));
        end
        
        if norm(x_new - x) < tol
            break;
        end
        
        x = x_new;
        iter = iter + 1;
    end
    
    if iter == max_iter
        disp("SOR迭代法未收敛！");
    end
end

这些代码可以作为一个函数使用，传入系数矩阵A，右侧常数项b，初始解向量x0，容差tol和最大迭代次数max_iter。函数会返回迭代得到的解向量x以及迭代次数iter。