Solving shifted linear systems with restarted GMRES augmented with error approximations

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 all...

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Published in:Computers & mathematics with applications (1987) 2019-09, Vol.78 (6), p.1910-1918
Main Authors: Wang, Rui-Rui, Niu, Qiang, Tang, Xiao-Bin, Wang, Xiang
Format: Article
Language:English
Subjects:
Acceleration
Added linear systems
Error analysis
Iterative methods
Krylov subspace methods
Linear systems
Mathematical analysis
Matrix algebra
Matrix methods
Multiplication
Restarted GMRES
Restarting
Subspaces
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container_end_page 1918
container_issue 6
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container_title Computers & mathematics with applications (1987)
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creator Wang, Rui-Rui
Niu, Qiang
Tang, Xiao-Bin
Wang, Xiang
description 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.
doi_str_mv 10.1016/j.camwa.2019.03.037
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subjects Acceleration
Added linear systems
Error analysis
Iterative methods
Krylov subspace methods
Linear systems
Mathematical analysis
Matrix algebra
Matrix methods
Multiplication
Restarted GMRES
Restarting
Subspaces
title Solving shifted linear systems with restarted GMRES augmented with error approximations
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