A flexible and adaptive Simpler GMRES with deflated restarting for shifted linear systems

Hong-Xiu Zhong; Xian-Ming Gu

doi:10.1016/j.camwa.2019.03.017

A flexible and adaptive Simpler GMRES with deflated restarting for shifted linear systems

Hong-Xiu Zhong, Xian-Ming Gu^*

^*Corresponding author for this work

Computational and Numerical Mathematics

Research output: Contribution to journal › Article › Academic › peer-review

7 Citations (Scopus)

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Abstract

In this paper, two efficient iterative algorithms based on the Simpler GMRES method are proposed for solving shifted linear systems. To make full use of the shifted structure, the proposed algorithms utilizing the deflated restarting strategy and flexible preconditioning can significantly reduce the number of matrix vector products and the elapsed CPU time. Numerical experiments are reported to illustrate the performance and effectiveness of the proposed algorithms. (C) 2019 Elsevier Ltd. All rights reserved.

Original language	English
Pages (from-to)	997-1007
Number of pages	11
Journal	Computers & Mathematics with Applications
Volume	78
Issue number	3
DOIs	https://doi.org/10.1016/j.camwa.2019.03.017
Publication status	Published - 1-Aug-2019

Keywords

Shifted linear system
Adaptive Simpler GMRES
Flexible preconditioning
Deflated restarting
BLOCK-GMRES
ALGORITHM
FAMILIES

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10.1016/j.camwa.2019.03.017

A flexible and adaptive Simpler GMRES with deflated restarting for shifted linear systemsFinal publisher's version, 466 KBLicence: Taverne

http://arxiv.org/pdf/1707.05588Licence: Unspecified

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title = "A flexible and adaptive Simpler GMRES with deflated restarting for shifted linear systems",

abstract = "In this paper, two efficient iterative algorithms based on the Simpler GMRES method are proposed for solving shifted linear systems. To make full use of the shifted structure, the proposed algorithms utilizing the deflated restarting strategy and flexible preconditioning can significantly reduce the number of matrix vector products and the elapsed CPU time. Numerical experiments are reported to illustrate the performance and effectiveness of the proposed algorithms. (C) 2019 Elsevier Ltd. All rights reserved.",

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AU - Zhong, Hong-Xiu

AU - Gu, Xian-Ming

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N2 - In this paper, two efficient iterative algorithms based on the Simpler GMRES method are proposed for solving shifted linear systems. To make full use of the shifted structure, the proposed algorithms utilizing the deflated restarting strategy and flexible preconditioning can significantly reduce the number of matrix vector products and the elapsed CPU time. Numerical experiments are reported to illustrate the performance and effectiveness of the proposed algorithms. (C) 2019 Elsevier Ltd. All rights reserved.

AB - In this paper, two efficient iterative algorithms based on the Simpler GMRES method are proposed for solving shifted linear systems. To make full use of the shifted structure, the proposed algorithms utilizing the deflated restarting strategy and flexible preconditioning can significantly reduce the number of matrix vector products and the elapsed CPU time. Numerical experiments are reported to illustrate the performance and effectiveness of the proposed algorithms. (C) 2019 Elsevier Ltd. All rights reserved.

KW - Shifted linear system

KW - Adaptive Simpler GMRES

KW - Flexible preconditioning

KW - Deflated restarting

KW - BLOCK-GMRES

KW - ALGORITHM

KW - FAMILIES

U2 - 10.1016/j.camwa.2019.03.017

DO - 10.1016/j.camwa.2019.03.017

M3 - Article

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JO - Computers & Mathematics with Applications

JF - Computers & Mathematics with Applications

IS - 3

ER -

A flexible and adaptive Simpler GMRES with deflated restarting for shifted linear systems

Abstract

Keywords

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