Open Access
October 2009 Fast Verified Solutions of Linear Systems
Takeshi Ogita, Shin'ichi Oishi
Japan J. Indust. Appl. Math. 26(2-3): 169-190 (October 2009).


This paper aims to survey fast methods of verifying the accuracy of a numerical solution of a linear system. For the last decade, a number of fast verification algorithms have been proposed to obtain an error bound of a numerical solution of a dense or sparse linear system. Such fast algorithms rely on the verified numerical computation using floating-point arithmetic defined by IEEE standard 754. Some fast verification methods for dense and sparse linear systems are reviewed together with corresponding numerical results to show the practical use and efficiency of the verified numerical computation as much as possible.


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Takeshi Ogita. Shin'ichi Oishi. "Fast Verified Solutions of Linear Systems." Japan J. Indust. Appl. Math. 26 (2-3) 169 - 190, October 2009.


Published: October 2009
First available in Project Euclid: 1 February 2010

zbMATH: 1184.65046
MathSciNet: MR2589471

Keywords: self-validating methods , verified numerical computation , verified solutions of linear systems

Rights: Copyright © 2009 The Japan Society for Industrial and Applied Mathematics

Vol.26 • No. 2-3 • October 2009
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