The Matrix Computation Toolbox
11 Sep 2002
11 Sep 2002)
A collection of M-files for carrying out various numerical linear algebra tasks.
function [Q, R] = gs_m(A)
%GS_M Modified Gram-Schmidt QR factorization.
% [Q, R] = GS_M(A) uses the modified 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.
% 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);
R(k,k) = norm(A(:,k));
Q(:,k) = A(:,k)/R(k,k);
R(k,k+1:n) = Q(:,k)'*A(:,k+1:n);
A(:,k+1:n) = A(:,k+1:n) - Q(:,k)*R(k,k+1:n);