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Numerical Algorithms

, Volume 80, Issue 2, pp 485–519 | Cite as

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

  • Zheng-Ge Huang
  • Li-Gong WangEmail author
  • Zhong Xu
  • Jing-Jing Cui
Original Paper
  • 55 Downloads

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.

Keywords

Saddle point problem MPHSS method Convergence Semi-convergence Preconditioning 

Mathematics Subject Classification (2010)

65F10 65F50 

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Notes

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 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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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Zheng-Ge Huang
    • 1
  • Li-Gong Wang
    • 1
    Email author
  • Zhong Xu
    • 1
  • Jing-Jing Cui
    • 1
  1. 1.School of Science, Department of Applied MathematicsNorthwestern Polytechnical UniversityXi’anPeople’s Republic of China

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