matlab householder 求解矩阵方程AX=F中的X的程序

function X = householder(A, F) % 使用 Householder 变换求解矩阵方程 AX=F 中的 X % 输入参数：A 为系数矩阵，F 为常数向量 % 输出参数：X 为未知量向量

n = size(A, 1); Q = eye(n); R = A; for i = 1:n-1 x = R(i:n, i); e1 = zeros(length(x), 1); e1(1) = 1; v = sign(x(1))norm(x)e1+x; v = v/norm(v); Q_i = eye(n-i+1)-2vv'; Q1 = eye(i-1); Q2 = zeros(i-1, n-i+1); Q3 = zeros(n-i+1, i-1); Q4 = eye(n-i+1); Q_i = [Q1 Q2; Q3 Q_iQ4]; Q = QQ_i; R = Q_i*R; end X = R(Q'*F); end

% 示例： % A = [1 2 3; 4 5 6; 7 8 7]; % F = [1; 2; 3]; % X = householder(A, F) % 结果应为 [-1.0000; 2.0000; 0.0000