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Modified quasi-Chebyshev acceleration to nonoverlapping parallel multisplitting method

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Abstract

In this study, we propose a modified quasi-Chebyshev acceleration to the nonoverlopping multisplitting iteration method for solving the linear systems A x = b where A is a real symmetric positive definite matrix or an H-matrix. In the process of the parallel multisplitting method, the distributive tasks are parallelly computed by each processor, then a global modified acceleration is used to obtain the solution of the system A x = b for every τ steps, such that the efficiency of the computation can be improved. The convergence theory of the new algorithm is given under some reasonable conditions. Finally, numerical experiments show that the method is efficient and effective.

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Authors and Affiliations

  1. Higher Education Key Laboratory of Engineering and Scientific Computing in Shanxi Province, Taiyuan Normal University, Taiyuan, 030012, Shanxi Province, People’s Republic of China

    Rui-Ping Wen

  2. Department of Mathematics, Taiyuan Normal University, Taiyuan, 030012, Shanxi Province, People’s Republic of China

    Fu-Jiao Ren

  3. Department of Mathmatics, Xinzhou Normal University, Xinzhou, 034000, Shanxi Province, People’s Republic of China

    Guo-Yan Meng

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  1. Rui-Ping Wen
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  2. Fu-Jiao Ren
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  3. Guo-Yan Meng
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Correspondence to Rui-Ping Wen.

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Wen, RP., Ren, FJ. & Meng, GY. Modified quasi-Chebyshev acceleration to nonoverlapping parallel multisplitting method. Numer Algor 75, 1123–1140 (2017). https://doi.org/10.1007/s11075-016-0234-4

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  • DOI: https://doi.org/10.1007/s11075-016-0234-4

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