matlab高斯消元法

Question

matlab代码怎么写(ﾟoﾟ;
用普通高斯消元，再用选主元高斯消元

Answer 1

以义 下午好🌅🌅🌅
本答案参考ChatGPT-3.5

以下是使用Matlab编写顺序高斯消元法和列主元高斯消元法的示例代码：

顺序高斯消元法：

function x = gaussian_elimination(A, b)
    [n, ~] = size(A);
    
    % 步骤1: 构造增广矩阵
    Aug = [A, b];
    
    % 步骤2: 前向消元
    for k = 1:n-1
        for i = k+1:n
            factor = Aug(i,k)/Aug(k,k);
            Aug(i,:) = Aug(i,:) - factor * Aug(k,:);
        end
    end
    
    % 步骤3: 回代求解
    x = zeros(n,1);
    x(n) = Aug(n,n+1) / Aug(n,n);
    for k = n-1:-1:1
        x(k) = (Aug(k,n+1) - Aug(k,k+1:n)*x(k+1:n)) / Aug(k,k);
    end
end

% 示例代码
A = [1.1348 3.8326; 1.1651 3.4017; 9.5342 0.5301; 1.7875 2.5330; 1.5435 6.3941];
b = [3.4129; 4.9317; 8.7643; 1.3142; 18.4231];

x = gaussian_elimination(A, b);
x = round(x, 5) % 结果保留小数点后5位

列主元高斯消元法：

function x = gaussian_elimination_pivot(A, b)
    [n, ~] = size(A);
    
    % 步骤1: 构造增广矩阵
    Aug = [A, b];
    
    % 步骤2: 前向消元（选择列主元）
    for k = 1:n-1
        [~, pivot] = max(abs(Aug(k:n,k)));
        pivot = pivot + k - 1;
        Aug([k,pivot],:) = Aug([pivot,k],:);
        
        for i = k+1:n
            factor = Aug(i,k)/Aug(k,k);
            Aug(i,:) = Aug(i,:) - factor * Aug(k,:);
        end
    end
    
    % 步骤3: 回代求解
    x = zeros(n,1);
    x(n) = Aug(n,n+1) / Aug(n,n);
    for k = n-1:-1:1
        x(k) = (Aug(k,n+1) - Aug(k,k+1:n)*x(k+1:n)) / Aug(k,k);
    end
end

% 示例代码
A = [1.1348 3.8326; 1.1651 3.4017; 9.5342 0.5301; 1.7875 2.5330; 1.5435 6.3941];
b = [3.4129; 4.9317; 8.7643; 1.3142; 18.4231];

x = gaussian_elimination_pivot(A, b);
x = round(x, 5) % 结果保留小数点后5位

请注意以上代码是一种简单的实现方式，可能并不适用于所有情况。在实际应用中，可能需要对代码进行修改以进行错误处理、输入验证和性能优化等。