function [x,iter] = GS(A,b,max_iter,tol) n = size(A,1); x = x0; iter = 0; while iter < max_iter for i = 1:n x(i) = b(i); for j = 1:i-1 x(i) = x(i) - A(i,j)*x(j); end for j = i+1:n x(i) = x(i) - A(i,j)*x(j); end %x(i) = x(i) + A(i,i)* x(i); x(i) = x(i) / A(i,i); end err = norm(A*x-b,Inf); fprintf('Step %d Error = %.2e\n',iter, err); disp(x); if err < tol break; end iter = iter +1 ; end end>> Demo3_Jacobi 函数或变量 'x0' 无法识别。 出错 Demo3_Jacobi>GS (第 15 行) x = x0; 出错 Demo3_Jacobi (第 7 行) [x,iter] = GS(A,b,max_iter,tol); >> Demo3_Jacobi 函数或变量 'x0' 无法识别。 出错 Demo3_Jacobi>GS (第 15 行) x = x0; 出错 Demo3_Jacobi (第 7 行) [x,iter] = GS(A,b,max_iter,tol);

这段代码是一个使用 Gauss-Seidel 迭代法求解线性方程组的函数，其中 A 是系数矩阵，b 是右端向量，_iter 是最大迭代数，tol 是收敛误差。但是出错提示说变量 x0 未定义，可能是在调用该函数时没有传入初始值 x0。因此需要在调用该函数时传入一个初始值 x0，其大小应该与 b 相同。

相关问题

A = [10 -1 -2; -1 10 -2; -1 -1 5]; b = [7.2; 8.3 ; 4.2]; max_iter = 30; tol = 1.0e-6; % [x,iter] = jacobi(A,b,max_iter,tol); [x,iter] = GS(A,b,max_iter,tol); %% Jacobi method % A: 矩阵 % b: 右端项 % max_iter: 最大迭代步数 function [x,iter] = jacobi(A,b,max_iter,tol) n = size(A,1); x = zeros(n,1); x_pre = x; iter = 0; while iter < max_iter for i = 1:n x(i) = b(i); for j = 1:n x(i) = x(i) - A(i,j)*x_pre(j); end x(i) = x(i) + A(i,i)* x_pre(i); x(i) = x(i) / A(i,i); end err = norm(A*x-b,Inf); fprintf('Step %d Error = %.2e\n',iter, err); if err < tol break; end x_pre = x; iter = iter +1 ; end end %% Gauss-Seidel method % A: 矩阵 % b: 右端项 % max_iter: 最大迭代步数 function [x,iter] = GS(A,b,max_iter,tol) n = size(A,1); x = zeros(n,1); iter = 0; while iter < max_iter for i = 1:n x(i) = b(i); for j = 1:i-1 x(i) = x(i) - A(i,j)*x(j); end for j = i+1:n x(i) = x(i) - A(i,j)*x(j); end %x(i) = x(i) + A(i,i)* x(i); x(i) = x(i) / A(i,i); end err = norm(A*x-b,Inf); fprintf('Step %d Error = %.2e\n',iter, err); if err < tol break; end iter = iter +1 ; end end如何给这段代码加上初值x0

可以在函数定义时增加一个参数x0，表示初始值，然后在迭代过程中将x_pre初始化为x0即可。修改后的代码如下：

%% Jacobi method
% A: 矩阵
% b: 右端项
% max_iter: 最大迭代步数
% tol: 收敛精度
% x0: 初始值
function [x,iter] = jacobi(A,b,max_iter,tol,x0)
n = size(A,1);
x = x0; % 将初始值赋给x
x_pre = x;
iter = 0;

while iter < max_iter
for i = 1:n
x(i) = b(i);
for j = 1:n
if j ~= i
x(i) = x(i) - A(i,j)*x_pre(j);
end
end
x(i) = x(i) / A(i,i);
end
err = norm(A*x-b,Inf);
fprintf('Step %d Error = %.2e\n',iter, err);
if err < tol
break;
end
x_pre = x;
iter = iter +1 ;
end
end

%% Gauss-Seidel method
% A: 矩阵
% b: 右端项
% max_iter: 最大迭代步数
% tol: 收敛精度
% x0: 初始值
function [x,iter] = GS(A,b,max_iter,tol,x0)
n = size(A,1);
x = x0; % 将初始值赋给x
iter = 0;

while iter < max_iter
for i = 1:n
x(i) = b(i);
for j = 1:i-1
x(i) = x(i) - A(i,j)*x(j);
end
for j = i+1:n
x(i) = x(i) - A(i,j)*x_pre(j);
end
x(i) = x(i) / A(i,i);
end
err = norm(A*x-b,Inf);
fprintf('Step %d Error = %.2e\n',iter, err);
if err < tol
break;
end
iter = iter +1 ;
end
end

调用时只需要传入一个初始值即可：

x0 = [1;2;3];
[x_jacobi, iter_jacobi] = jacobi(A, b, max_iter, tol, x0);
[x_gs, iter_gs] = GS(A, b, max_iter, tol, x0);

修改function [x, iter] = jacobi(A, b, x0, tol, max_iter) function main() n = 10; % 矩阵维度 A = generatePentaDiagonalMatrix(n); % 生成五对角矩阵 x0 = zeros(n, 1); % 初始向量 b = ones(n, 1); % 右端向量 tol = 1e-6; % 迭代误差要求 % 使用Jacobi迭代法求解 [x_jacobi, iter_jacobi] = jacobi(A, b, x0, tol, 1000); fprintf("Jacobi迭代法 - 迭代次数: %d\n", iter_jacobi); % 使用Gauss-Seidel迭代法求解 end function A = generatePentaDiagonalMatrix(n) % 生成五对角矩阵 diag_main = 3 * ones(n, 1); diag_sub = -1/2 * ones(n-1, 1); diag_super = -1/2 * ones(n-1, 1); diag_sub_sub = -1/4 * ones(n-2, 1); diag_super_super = -1/4 * ones(n-2, 1); A = diag(diag_main) + diag(diag_sub, -1) + diag(diag_super, 1) + diag(diag_sub_sub, -2) + diag(diag_super_super, 2); end 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

修改后的代码如下：

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

function main()
    n = 10; % 矩阵维度
    A = generatePentaDiagonalMatrix(n); % 生成五对角矩阵
    x0 = zeros(n, 1); % 初始向量
    b = ones(n, 1); % 右端向量
    tol = 1e-6; % 迭代误差要求
    
    % 使用Jacobi迭代法求解
    [x_jacobi, iter_jacobi] = jacobi(A, b, x0, tol, 1000);
    fprintf("Jacobi迭代法 - 迭代次数: %d\n", iter_jacobi);
    
    % 使用Gauss-Seidel迭代法求解
    [x_gs, iter_gs] = gaussSeidel(A, b, x0, tol, 1000);
    fprintf("Gauss-Seidel迭代法 - 迭代次数: %d\n", iter_gs);
end

function A = generatePentaDiagonalMatrix(n)
    % 生成五对角矩阵
    diag_main = 3 * ones(n, 1);
    diag_sub = -1/2 * ones(n-1, 1);
    diag_super = -1/2 * ones(n-1, 1);
    diag_sub_sub = -1/4 * ones(n-2, 1);
    diag_super_super = -1/4 * ones(n-2, 1);

    A = diag(diag_main) + diag(diag_sub, -1) + diag(diag_super, 1) + diag(diag_sub_sub, -2) + diag(diag_super_super, 2);
end

在`main`函数中，我添加了使用Gauss-Seidel迭代法求解的部分。你可以根据需要填充该部分的代码。同时，我还修复了代码末尾的错误，将闭合的`end`移到正确的位置。