matlab householder 求解矩阵方程AX=F 的程序 A为mn矩阵 mn

function [x] = householder(A, F) % A为mn矩阵，F为m1向量，m<n [m, n] = size(A); % 初始化矩阵Q和R Q = eye(m); R = A; % 对每一列进行Householder变换 for k = 1:n x = R(k:m, k); v = x; v(1) = v(1) + sign(x(1)) * norm(x); v = v / norm(v); % 更新R矩阵 R(k:m, k:n) = R(k:m, k:n) - 2 * v * (v' * R(k:m, k:n)); % 更新Q矩阵 Q(k:m, :) = Q(k:m, :) - 2 * v * (v' * Q(k:m, :)); end % 解方程Ax=F y = Q' * F; x = R \ y; end