Accurate solution of dense linear systems. II: Algorithms using directed rounding
type: Item
instance of: scholarly article
title: Accurate solution of dense linear systems. II: Algorithms using directed rounding
zbMATH Open document ID: 1260.65034
published in: Journal of Computational and Applied Mathematics
publication date: 2013-01-21T00:00:00Z
review text: The author investigates how extra-precise evaluation of dot products can be used to solve ill-conditioned linear systems rigorously and accurately. Moreover, in this Part II of it they use directed rounding to nearest and methods different from the four basic floating-point operations. For Part I see [ibid. 242, 157--184 (2013; Zbl 1255.65084)].
Mathematics Subject Classification ID: 65F22
Mathematics Subject Classification ID: 65F05
Mathematics Subject Classification ID: 65G20
zbMATH DE Number: 6127784
zbMATH Keywords: linear systems
zbMATH Keywords: data with tolerances
zbMATH Keywords: inner bounds
zbMATH Keywords: (extremely) ill-conditioned matrices
zbMATH Keywords: rigorous error bounds
zbMATH Keywords: ill-conditioned linear systems
author: Siegfried M. Rump
reviewed by: Constantin Popa
describes a project that uses: INTLIB
describes a project that uses: Matlab
describes a project that uses: VERSOFT
describes a project that uses: PROFIL/BIAS
describes a project that uses: INTLAB
describes a project that uses: b4m
MaRDI profile type: Publication
full work available at URL: j.cam.2012.09.024
OpenAlex ID: W2024194142
DOI: 10.1016/J.CAM.2012.09.024
description: scientific article; zbMATH DE number 6127784