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On \({\varvec{m}}\)-step Hermitian and skew-Hermitian splitting preconditioning methods

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Abstract

Preconditioners are often applied in various Krylov subspace iteration methods to improve their computing efficiency. In this paper, we consider solving linear systems with a non-Hermitian positive definite coefficient matrix using preconditioned Krylov subspace iteration methods such as the generalized minimal residual (GMRES) method. An \(m\)-step polynomial preconditioner is designed based on the Hermitian and skew-Hermitian splitting (HSS) iteration method proposed by Bai et al. (SIAM J Matrix Anal Appl 24:603–626, 2003). The proposed preconditioned system is solved by fully utilizing the HSS iteration method. Theoretical and experimental results show that the proposed \(m\)-step preconditioner is efficient in accelerating GMRES for solving a non-Hermitian positive definite linear system.

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Acknowledgments

Research supported in part by NSFC Grant 11101195 and China Postdoctoral Science Foundation funded Project 2011M501488.

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  1. School of Mathematics and Statistics, Lanzhou University, Lanzhou , 730000, Gansu, People’s Republic of China

    Yu-Mei Huang

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  1. Yu-Mei Huang
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Correspondence to Yu-Mei Huang.

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Huang, YM. On \({\varvec{m}}\)-step Hermitian and skew-Hermitian splitting preconditioning methods. J Eng Math 93, 77–86 (2015). https://doi.org/10.1007/s10665-013-9676-z

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  • DOI: https://doi.org/10.1007/s10665-013-9676-z

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