Improved backward error bounds for LU and Cholesky factorizations
type: Item
instance of: scholarly article
zbMATH Open document ID: 1309.65031
DOI: 10.1137/130927231
author: Claude-Pierre Jeannerod
author: Siegfried M. Rump
published in: SIAM Journal on Matrix Analysis and Applications
publication date: 2014-10-15T00:00:00Z
full work available at URL: RumpJeannerod14.pdf
Mathematics Subject Classification ID: 65F05
Mathematics Subject Classification ID: 65G50
zbMATH DE Number: 6356192
zbMATH Keywords: LU factorization
zbMATH Keywords: Cholesky factorization
zbMATH Keywords: floating-point summation
zbMATH Keywords: rounding error analysis
zbMATH Keywords: triangular system solving
zbMATH Keywords: backward error bound
Wikidata QID: Q114074343
MaRDI profile type: Publication
OpenAlex ID: W2047319360
title: Improved backward error bounds for LU and Cholesky factorizations
review text: New backward error bounds for LU and Cholesky factorizations are provided. To get these new bounds, the main ingradient is a refinement of the well-known Lemma 8.4 from \textit{N. J. Higham} [Accuracy and stability of numerical algorithms. 2nd ed. Philadelphia, PA: SIAM (2002; Zbl 1011.65010)] via some careful rounding error analysis of sums of one floating-point number and \(n-1\) real numbers.
reviewed by: Liu Xinguo
description: scientific article; zbMATH DE number 6356192