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On the accelerated modified Newton-HSS method for systems of nonlinear equations

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Abstract

Hermitian and skew-Hermitian splitting (HSS) method converges unconditionally, which is efficient and robust for solving non-Hermitian positive-definite systems of linear equations. For solving systems of nonlinear equations with non-Hermitian positive-definite Jacobian matrices, Bai and Guo proposed the Newton-HSS method and gave numerical comparisons to show that the Newton-HSS method is superior to the Newton-USOR, the Newton-GMRES and the Newton-GCG methods. Recently, Wu and Chen proposed the modified Newton-HSS (MN-HSS) method which outperformed the Newton-HSS method. In this paper, we will establish a new accelerated modified Newton-HSS (AMN-HSS) method and give the local convergence theorem. Moreover, numerical results show that the AMN-HSS method outperforms the MN-HSS method.

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Acknowledgments

The authors are very much indebted to the referees for their constructive and valuable comments and suggestions which greatly improved the original version of this paper.

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Authors and Affiliations

  1. Department of Mathematics, East China Normal University, Shanghai, 200241, People’s Republic of China

    Ya-Min Li & Xue-Ping Guo

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  1. Ya-Min Li
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  2. Xue-Ping Guo
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Correspondence to Xue-Ping Guo.

Additional information

This work was partly supported by National Natural Science Foundation of China (11471122, 11371145), Science and Technology Commission of Shanghai Municipality (STCSM, 13dz2260400).

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Li, YM., Guo, XP. On the accelerated modified Newton-HSS method for systems of nonlinear equations. Numer Algor 79, 1049–1073 (2018). https://doi.org/10.1007/s11075-018-0472-8

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  • DOI: https://doi.org/10.1007/s11075-018-0472-8

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