Solving shifted linear systems with restarted GMRES augmented with error approximations

Rui Rui Wang; Qiang Niu; Xiao Bin Tang; Xiang Wang

doi:10.1016/j.camwa.2019.03.037

Solving shifted linear systems with restarted GMRES augmented with error approximations

Rui Rui Wang, Qiang Niu, Xiao Bin Tang, Xiang Wang^*

^*Corresponding author for this work

Department of Applied Mathematics

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

2 Citations (Scopus)

Abstract

In this paper, we investigate a variant of the restarted GMRES method for solving a series of large sparse linear systems. Restarting is carried out by augmenting Krylov subspaces with some recently generated error approximations from the seed system. The method can preserve a nice property that allows solving the seed and the added linear systems at the cost of only one matrix–vector multiplication per iteration. Compared with solving each added linear system separately, the advantage of the new scheme is to lower down the overall cost of solving all added linear systems. Numerical experiments illustrate the efficiency of the acceleration strategy.

Original language	English
Pages (from-to)	1910-1918
Number of pages	9
Journal	Computers and Mathematics with Applications
Volume	78
Issue number	6
DOIs	https://doi.org/10.1016/j.camwa.2019.03.037
Publication status	Published - 15 Sept 2019

Keywords

Added linear systems
Krylov subspace methods
Restarted GMRES

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10.1016/j.camwa.2019.03.037

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abstract = "In this paper, we investigate a variant of the restarted GMRES method for solving a series of large sparse linear systems. Restarting is carried out by augmenting Krylov subspaces with some recently generated error approximations from the seed system. The method can preserve a nice property that allows solving the seed and the added linear systems at the cost of only one matrix–vector multiplication per iteration. Compared with solving each added linear system separately, the advantage of the new scheme is to lower down the overall cost of solving all added linear systems. Numerical experiments illustrate the efficiency of the acceleration strategy.",

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author = "Wang, {Rui Rui} and Qiang Niu and Tang, {Xiao Bin} and Xiang Wang",

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AU - Wang, Rui Rui

AU - Niu, Qiang

AU - Tang, Xiao Bin

AU - Wang, Xiang

PY - 2019/9/15

Y1 - 2019/9/15

N2 - In this paper, we investigate a variant of the restarted GMRES method for solving a series of large sparse linear systems. Restarting is carried out by augmenting Krylov subspaces with some recently generated error approximations from the seed system. The method can preserve a nice property that allows solving the seed and the added linear systems at the cost of only one matrix–vector multiplication per iteration. Compared with solving each added linear system separately, the advantage of the new scheme is to lower down the overall cost of solving all added linear systems. Numerical experiments illustrate the efficiency of the acceleration strategy.

AB - In this paper, we investigate a variant of the restarted GMRES method for solving a series of large sparse linear systems. Restarting is carried out by augmenting Krylov subspaces with some recently generated error approximations from the seed system. The method can preserve a nice property that allows solving the seed and the added linear systems at the cost of only one matrix–vector multiplication per iteration. Compared with solving each added linear system separately, the advantage of the new scheme is to lower down the overall cost of solving all added linear systems. Numerical experiments illustrate the efficiency of the acceleration strategy.

KW - Added linear systems

KW - Krylov subspace methods

KW - Restarted GMRES

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JO - Computers and Mathematics with Applications

JF - Computers and Mathematics with Applications

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ER -

Solving shifted linear systems with restarted GMRES augmented with error approximations

Abstract

Keywords

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