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Minimum residual Hermitian and skew-Hermitian splitting iteration method for non-Hermitian positive definite linear systems

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Abstract

By applying the minimum residual technique to the Hermitian and skew-Hermitian splitting (HSS) iteration scheme, we introduce a non-stationary iteration method named minimum residual HSS (MRHSS) iteration method to solve non-Hermitian positive definite linear systems. The convergence property of the MRHSS iteration method together with the property of the iteration parameters are carefully studied. Numerical results verify the effectiveness and robustness of the MRHSS iteration method.

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Acknowledgements

The authors are very much indebted to the referees for their constructive and valuable comments and suggestions which greatly improved the quality of this paper. This work is partially supported by the National Key Research and Development Program of China (Grant No. 2018YFC0406600) and the National Natural Science Foundation of China (Grant Nos. 11471150, 11771225, 11401281).

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Authors and Affiliations

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

    Ai-Li Yang & Yu-Jiang Wu

  2. School of Transportation, Nantong University, Nantong, 226019, Jiangsu, People’s Republic of China

    Yang Cao

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  1. Ai-Li Yang
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  2. Yang Cao
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Correspondence to Ai-Li Yang.

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Communicated by Lars Eldén.

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Yang, AL., Cao, Y. & Wu, YJ. Minimum residual Hermitian and skew-Hermitian splitting iteration method for non-Hermitian positive definite linear systems. Bit Numer Math 59, 299–319 (2019). https://doi.org/10.1007/s10543-018-0729-6

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