A generalized Shift-HSS splitting method for nonsingular saddle point problems

Zhuo-Hong Huang; Zhuo-Hong Huang

doi:10.3934/math.2022747

AIMS Mathematics

2022, Volume 7, Issue 7: 13508-13536. doi: 10.3934/math.2022747

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Research article

A generalized Shift-HSS splitting method for nonsingular saddle point problems

Zhuo-Hong Huang ^{1,2
,
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1.
School of Science, Chongqing University of Technology, Chongqing, 400054, China
2.
School of Mathematics and Physics, Guangxi Minzu University, Nanning, 530006, China

Received: 23 April 2022 Accepted: 05 May 2022 Published: 20 May 2022
MSC : 65F08, 65F10

In this paper, we propose a generalized shift-HSS (denoted by SFHSS) iteration method for solving nonsingular saddle point systems with nonsymmetric positive definite (1, 1)-block sub-matrix, and theoretically verify its convergence property. In addition, we discuss the algebraic properties of the resulted SFHSS preconditioner and estimate the sharp eigenvalue bounds of the related preconditioned matrix. Finally, numerical experiments are given to support our theoretical results and reveal that the new method is feasible and effective.
- generalized shift-HSS splitting,
- convergence property,
- nonsymmetric positive definite,
- nonsingular,
- Krylov subspace methods
Citation: Zhuo-Hong Huang. A generalized Shift-HSS splitting method for nonsingular saddle point problems[J]. AIMS Mathematics, 2022, 7(7): 13508-13536. doi: 10.3934/math.2022747

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Abstract

In this paper, we propose a generalized shift-HSS (denoted by SFHSS) iteration method for solving nonsingular saddle point systems with nonsymmetric positive definite (1, 1)-block sub-matrix, and theoretically verify its convergence property. In addition, we discuss the algebraic properties of the resulted SFHSS preconditioner and estimate the sharp eigenvalue bounds of the related preconditioned matrix. Finally, numerical experiments are given to support our theoretical results and reveal that the new method is feasible and effective.

References

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