A note on the error analysis of classical Gram-Schmidt
Abstract
An error analysis result is given for classical Gram--Schmidt factorization of a full rank matrix into where is left orthogonal (has orthonormal columns) and is upper triangular. The work presented here shows that the computed satisfies where is an appropriately small backward error, but only if the diagonals of are computed in a manner similar to Cholesky factorization of the normal equations matrix. A similar result is stated in [Giraud at al, Numer. Math. 101(1):87--100,2005]. However, for that result to hold, the diagonals of must be computed in the manner recommended in this work.
Keywords
Cite
@article{arxiv.math/0606258,
title = {A note on the error analysis of classical Gram-Schmidt},
author = {Alicja Smoktunowicz and Jesse L. Barlow and Julien Langou},
journal= {arXiv preprint arXiv:math/0606258},
year = {2008}
}
Comments
12 pages This v2. v1 (from 2006) has not the biliographical reference set (at all). This is the only modification between v1 and v2. If you want to quote this paper, please quote the version published in Numerische Mathematik