www.gusucode.com > 矩阵计算工具箱 - mctoolbox源码程序 > matrixcomp\gs_c.m
function [Q, R] = gs_c(A) %GS_C Classical Gram-Schmidt QR factorization. % [Q, R] = GS_C(A) uses the classical Gram-Schmidt method to compute the % factorization A = Q*R for m-by-n A of full rank, % where Q is m-by-n with orthonormal columns and R is n-by-n. % Reference: % N. J. Higham, Accuracy and Stability of Numerical Algorithms, % Second edition, Society for Industrial and Applied Mathematics, % Philadelphia, PA, 2002; sec 19.8. [m, n] = size(A); Q = zeros(m,n); R = zeros(n); for j=1:n R(1:j-1,j) = Q(:,1:j-1)'*A(:,j); temp = A(:,j) - Q(:,1:j-1)*R(1:j-1,j); R(j,j) = norm(temp); Q(:,j) = temp/R(j,j); end