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Accelerated PMHSS iteration methods for complex symmetric linear systems

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Abstract

In this paper, we introduce and analyze an accelerated preconditioning modification of the Hermitian and skew-Hermitian splitting (APMHSS) iteration method for solving a broad class of complex symmetric linear systems. This accelerated PMHSS algorithm involves two iteration parameters α,β and two preconditioned matrices whose special choices can recover the known PMHSS (preconditioned modification of the Hermitian and skew-Hermitian splitting) iteration method which includes the MHSS method, as well as yield new ones. The convergence theory of this class of APMHSS iteration methods is established under suitable conditions. Each iteration of this method requires the solution of two linear systems with real symmetric positive definite coefficient matrices. Theoretical analyses show that the upper bound σ 1(α,β) of the asymptotic convergence rate of the APMHSS method is smaller than that of the PMHSS iteration method. This implies that the APMHSS method may converge faster than the PMHSS method. Numerical experiments on a few model problems are presented to illustrate the theoretical results and examine the numerical effectiveness of the new method.

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Authors and Affiliations

  1. School of Mathematics and Computer Science & FJKLMAA, Fujian Normal University, Fuzhou, 350007, People’s Republic of China

    Qing-Qing Zheng & Chang-Feng Ma

  2. School of Mathematical Science, Xiamen University, Xiamen, 361005, People’s Republic of China

    Qing-Qing Zheng

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  1. Qing-Qing Zheng
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  2. Chang-Feng Ma
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Correspondence to Chang-Feng Ma.

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Zheng, QQ., Ma, CF. Accelerated PMHSS iteration methods for complex symmetric linear systems. Numer Algor 73, 501–516 (2016). https://doi.org/10.1007/s11075-016-0105-z

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  • DOI: https://doi.org/10.1007/s11075-016-0105-z

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