A generalized Shift-HSS splitting method for nonsingular saddle point problems-Reference-Cited by-同舟云学术

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

Published:2022 Issue:7 Volume:7 Page:13508-13536
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Huang Zhuo-Hong¹²

Affiliation:

1. School of Science, Chongqing University of Technology, Chongqing, 400054, China

2. School of Mathematics and Physics, Guangxi Minzu University, Nanning, 530006, China

Abstract

<abstract><p>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.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

Reference35 articles.

1. M. Benzi, G. H. Golub, J. Liesen, Numerical solution of saddle point problems, Acta Numer., 14 (2005), 1–137. https://doi.org/10.1017/S0962492904000212

2. C. Q. Lv, C. F. Ma, BCR method for solving generalized coupled Sylvester equations over centrosymmetric or anti-centrosymmetric matrix, Comput. Math. Appl., 75 (2018), 70–88. https://doi.org/10.1016/j.camwa.2017.08.041

3. H. C. Elman, Preconditioning for the steady-state Navier-Stokes equations with low viscosity, SIAM J. Sci. Comput., 20 (1999), 1299–1316. https://doi.org/10.1137/S1064827596312547

4. Z. Z. Bai, B. N. Parlett, Z. Q. Wang, On generalized successive overrelaxation methods for augmented linear systems, Numer. Math., 102 (2005), 1–38. https://doi.org/10.1007/s00211-005-0643-0

5. S. L. Wu, T. Z. Huang, X. L. Zhao, A modified SSOR iterative method for augmented systems, J. Comput. Appl. Math., 228 (2009), 424–433. https://doi.org/10.1016/j.cam.2008.10.006