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On the m-step two-parameter generalized Hermitian and skew-Hermitian splitting preconditioning method

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Abstract

In this paper, the non-Hermitian positive definite linear systems are solved via preconditioned Krylov subspace methods such as the generalized minimal residual (GMRES) method. To do so, the two-parameter generalized Hermitian and skew-Hermitian splitting (TGHSS) iteration method is applied to establish an m-step polynomial preconditioner. Some theoretical results are also given to investigate the convergence properties of the preconditioned method. Three numerical examples are presented to demonstrate the performance of the new method and to compare it with a recently proposed method.

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Acknowledgements

The authors are grateful to anonymous referees and editor of the journal for their valuable comments and suggestions. The work of the second author is partially supported by University of Guilan.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Mathematical Sciences, University of Mohaghegh Ardabili, Ardabil, Iran

    Mehdi Bastani

  2. Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran

    Davod Khojasteh Salkuyeh

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  1. Mehdi Bastani
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  2. Davod Khojasteh Salkuyeh
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Correspondence to Mehdi Bastani.

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Bastani, M., Salkuyeh, D.K. On the m-step two-parameter generalized Hermitian and skew-Hermitian splitting preconditioning method. Afr. Mat. 28, 999–1010 (2017). https://doi.org/10.1007/s13370-017-0489-5

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  • DOI: https://doi.org/10.1007/s13370-017-0489-5

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