matlab写出所有作业代码

根据提供的文档内容，以下是需要编写的MATLAB作业代码：

### 1. Gauss消去法 (Gauss Elimination Method)

function x = Demo_4_1_Gauss_S(A, b)
    n = length(b);
    % 增广矩阵
    Ab = [A b];
    
    % 消元过程
    for k = 1:n-1
        for i = k+1:n
            factor = Ab(i,k) / Ab(k,k);
            Ab(i,k:n+1) = Ab(i,k:n+1) - factor * Ab(k,k:n+1);
        end
    end
    
    % 回代求解
    x = zeros(n,1);
    x(n) = Ab(n,n+1) / Ab(n,n);
    for i = n-1:-1:1
        x(i) = (Ab(i,n+1) - Ab(i,i+1:n) * x(i+1:n)) / Ab(i,i);
    end
end

### 2. 杜立特尔分解法 (Doolittle Decomposition)

function [L, U] = Demo_4_2_Doolittle(A)
    n = size(A, 1);
    L = eye(n);
    U = zeros(n);
    
    for k = 1:n
        U(k,k) = A(k,k) - L(k,1:k-1) * U(1:k-1,k);
        for j = k+1:n
            U(k,j) = A(k,j) - L(k,1:k-1) * U(1:k-1,j);
        end
        for i = k+1:n
            L(i,k) = (A(i,k) - L(i,1:k-1) * U(1:k-1,k)) / U(k,k);
        end
    end
end

### 3. 逐次超松弛迭代法 (Successive Over-Relaxation Iteration Method)

function x = Demo_6_2_Jacobi_G_S_SOR(A, b, w, tol, max_iter)
    n = length(b);
    x = zeros(n, 1); % 初始猜测
    x_new = zeros(n, 1);
    iter = 0;
    
    while true
        iter = iter + 1;
        for i = 1:n
            sigma = 0;
            for j = 1:n
                if j ~= i
                    sigma = sigma + A(i,j) * x(j);
                end
            end
            x_new(i) = (1 - w) * x(i) + (w / A(i,i)) * (b(i) - sigma);
        end
        
        if norm(x_new - x, inf) < tol || iter >= max_iter
            break;
        end
        
        x = x_new;
    end
end

### 使用示例
假设你需要解以下线性方程组：
\[ \begin{cases}
2x_1 + 3x_2 + 4x_3 = 6 \\
3x_1 + 5x_2 + 2x_3 = 5 \\
4x_1 + 3x_2 + 30x_3 = 32
\end{cases} \]

可以调用上述函数如下：

% 定义系数矩阵和常数向量
A = [2 3 4; 3 5 2; 4 3 30];
b = [6; 5; 32];

% 调用Gauss消去法
x_gauss = Demo_4_1_Gauss_S(A, b);

% 调用杜立特尔分解法
[L, U] = Demo_4_2_Doolittle(A);
y = L \ b;
x_doolittle = U \ y;

% 调用逐次超松弛迭代法
w = 1.2; % 超松弛因子
tol = 1e-6; % 容差
max_iter = 1000; % 最大迭代次数
x_sor = Demo_6_2_Jacobi_G_S_SOR(A, b, w, tol, max_iter);

disp('Gauss消去法结果:');
disp(x_gauss);

disp('杜立特尔分解法结果:');
disp(x_doolittle);

disp('逐次超松弛迭代法结果:');
disp(x_sor);

以上是根据文档内容编写的MATLAB代码，希望对你有帮助！