Extension of an approximate orthogonalization algorithm to arbitrary rectangular matrices

Z. Kovarik described in (SIAM J. Numer. Anal. 7 (3) (1970) 386] a method fo r approximate orthogonalization of a finite set of linearly independent vec tors from an arbitrary (real or complex) Hilbert space. In this paper, we g eneralize Kovariks method in the case when the vectors are rows (not necess ary linearly independent) of an arbitrary rectangular real matrix. In this case we prove that, both rows and columns of the matrix are transformed in vectors which are "quasi-orthogonal", in a sense that is clearly described. Numerical experiments are presented in the last section of the paper. (C) 2001 Elsevier Science Inc. All rights reserved.