The loss of orthogonality in the Gram-Schmidt orthogonalization process

Authors:
L. Giraud;J. Langou;M. Rozloznik
Affiliations:
-;-;-
Venue:
Computers & Mathematics with Applications
Year:
2005

Citing 7
Cited 1

GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems

SIAM Journal on Scientific and Statistical Computing
Iterative algorithms for Gram-Schmidt orthogonalization

Computing
Loss and recapture of orthogonality in the modified Gram-Schmidt algorithm

SIAM Journal on Matrix Analysis and Applications
Parallel implementation of a multiblock method with approximate subdomain solution

Applied Numerical Mathematics
Accuracy and Stability of Numerical Algorithms

Accuracy and Stability of Numerical Algorithms
On the Influence of the Orthogonalization Scheme on the Parallel Performance of GMRES

Euro-Par '98 Proceedings of the 4th International Euro-Par Conference on Parallel Processing
Rounding error analysis of the classical Gram-Schmidt orthogonalization process

Numerische Mathematik

Letter to the Editor: Experiments on orthogonalization by biorthogonal representations of orthogonal projectors

Journal of Computational and Applied Mathematics

Quantified Score

Hi-index	0.09

Visualization

Abstract

In this paper, we study numerical behavior of several computational variants of the Gram-Schmidt orthogonalization process. We focus on the orthogonality of computed vectors which may be significantly lost in the classical or modified Gram-Schmidt algorithm, while the Gram-Schmidt algorithm with reorthogonalization has been shown to compute vectors which are orthogonal to machine precision level. The implications for practical implementation and its impact on the efficiency in the parallel computer environment are considered.