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Modified PHSS iterative methods for solving nonsingular and singular saddle point problems

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Abstract

For large sparse saddle point problems, we establish a new version of the preconditioned Hermitian and skew-Hermitian splitting (PHSS) iteration method, called the modified PHSS (MPHSS) method in this paper. Then, we theoretically study its convergence and semi-convergence properties and determine its optimal iteration parameter and corresponding optimal convergence factor. Furthermore, the spectral properties of the MPHSS preconditioned matrix are discussed in detail. Numerical experiments show that the MPHSS iteration method is effective and robust when it is used either as a solver or as a matrix splitting preconditioner for the generalized minimal residual (GMRES) method.

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Acknowledgments

We would like to express our sincere thanks to the anonymous reviewer for his/her valuable suggestions and constructive comments which greatly improved the presentation of this paper.

Funding

This research was supported by the National Natural Science Foundation of China (No. 11171273) and sponsored by Innovation Foundation for Doctor Dissertation of Northwestern Polytechnical University (No. CX201628).

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Authors and Affiliations

  1. School of Science, Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an, 710072, Shaanxi, People’s Republic of China

    Zheng-Ge Huang, Li-Gong Wang, Zhong Xu & Jing-Jing Cui

Authors
  1. Zheng-Ge Huang
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  2. Li-Gong Wang
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  3. Zhong Xu
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  4. Jing-Jing Cui
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Corresponding author

Correspondence to Li-Gong Wang.

Additional information

This research was supported by the National Natural Science Foundation of China (No. 11171273) and sponsored by Innovation Foundation for Doctor Dissertation of Northwestern Polytechnical University (No. CX201628).

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Huang, ZG., Wang, LG., Xu, Z. et al. Modified PHSS iterative methods for solving nonsingular and singular saddle point problems. Numer Algor 80, 485–519 (2019). https://doi.org/10.1007/s11075-018-0494-2

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  • DOI: https://doi.org/10.1007/s11075-018-0494-2

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