Preconditioning for accurate solutions of ill-conditioned linear systems

Qiang Ye

doi:10.1002/nla.2315

Preconditioning for accurate solutions of ill-conditioned linear systems

Qiang Ye

Producción científica: Article › revisión exhaustiva

3 Citas (Scopus)

Resumen

This article develops the preconditioning technique as a method to address the accuracy issue caused by ill-conditioning. Given a preconditioner M for an ill-conditioned linear system Ax=b, we show that, if the inverse of the preconditioner M⁻¹ can be applied to vectors accurately, then the linear system can be solved accurately. A stability concept called inverse-equivalent accuracy is introduced to describe the high accuracy that is achieved and an error analysis will be presented. Numerical examples are presented to illustrate the error analysis and the performance of the methods.

Idioma original	English
Número de artículo	e2315
Publicación	Numerical Linear Algebra with Applications
Volumen	27
N.º	4
DOI	https://doi.org/10.1002/nla.2315
Estado	Published - ago 1 2020

Nota bibliográfica

Publisher Copyright:
© 2020 John Wiley & Sons, Ltd.

Financiación

The author would like to thank Prof. Jinchao Xu for some interesting discussions on multilevel preconditioners that have inspired this work. The author would also like to thank Kasey Bray for many helpful comments on a draft of this article and also like to thank anonymous referees for many detailed and insightful comments that have significantly improved the paper. This research was supported in part by NSF under Grants DMS‐1318633, DMS‐1620082, and DMS‐1821144. This work does not have any conflicts of interest. information NSF Division of Mathematical Sciences, 1318633; 1620082; 1821144The author would like to thank Prof. Jinchao Xu for some interesting discussions on multilevel preconditioners that have inspired this work. The author would also like to thank Kasey Bray for many helpful comments on a draft of this article and also like to thank anonymous referees for many detailed and insightful comments that have significantly improved the paper. This research was supported in part by NSF under Grants DMS-1318633, DMS-1620082, and DMS-1821144. This work does not have any conflicts of interest.

Financiadores	Número del financiador
National Science Foundation (NSF)	DMS‐1620082, 1821144, DMS‐1821144, DMS‐1318633
Division of Mathematical Sciences	1318633, 1620082

ASJC Scopus subject areas

Algebra and Number Theory
Applied Mathematics

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Preconditioning for accurate solutions of ill-conditioned linear systems

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