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Block GPBi-CG method for solving nonsymmetric linear systems with multiple right-hand sides and its convergence analysis

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Abstract

In this paper, the block generalized product-type bi-conjugate gradient (GPBi-CG) method for solving large, sparse nonsymmetric linear systems of equations with multiple right-hand sides is proposed. The new algorithm is based on the block BiCG process. We analyze the convergence behavior of this method and present a bound for the residual norm of block GPBi-CG according to the residual norm of Bl-GMRES method. In addition, we prove that convergence is guaranteed when A is positive real. The numerical experiments show the efficiency of the new method and confirm the theoretical results.

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Acknowledgements

We would like to thank the referees for their valuable remarks and helpful suggestions.

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Authors and Affiliations

  1. Department of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran

    A. Taherian & F. Toutounian

  2. The Center of Excellence on Modeling and Control Systems, Ferdowsi University of Mashhad, Mashhad, Iran

    F. Toutounian

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  1. A. Taherian
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  2. F. Toutounian
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Correspondence to F. Toutounian.

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Taherian, A., Toutounian, F. Block GPBi-CG method for solving nonsymmetric linear systems with multiple right-hand sides and its convergence analysis. Numer Algor 88, 1831–1850 (2021). https://doi.org/10.1007/s11075-021-01097-7

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  • DOI: https://doi.org/10.1007/s11075-021-01097-7

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Mathematics Subject Classification (2010)