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Multistep matrix splitting iteration preconditioning for singular linear systems

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Abstract

Multistep matrix splitting iterations serve as preconditioning for Krylov subspace methods for solving singular linear systems. The preconditioner is applied to the generalized minimal residual (GMRES) method and the flexible GMRES (FGMRES) method. We present theoretical and practical justifications for using this approach. Numerical experiments show that the multistep generalized shifted splitting (GSS) and Hermitian and skew-Hermitian splitting (HSS) iteration preconditioning are more robust and efficient compared to standard preconditioners for some test problems of large sparse singular linear systems.

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  1. Division of Information Engineering, Faculty of Engineering, Information and Systems, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki, 305-8573, Japan

    Keiichi Morikuni

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  1. Keiichi Morikuni
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Correspondence to Keiichi Morikuni.

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This work was supported by the Czech Academy of Sciences under No. M100301201 and JSPS KAKENHI Grant Number 16K17639.

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Morikuni, K. Multistep matrix splitting iteration preconditioning for singular linear systems. Numer Algor 75, 457–475 (2017). https://doi.org/10.1007/s11075-017-0330-0

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