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Title: On semi-convergence and inexact iteration of the GSS iteration method for nonsymmetric singular saddle point problems

Abstract

In this paper, the generalized shift-splitting (GSS) iteration method is used to solve nonsymmetric singular saddle point systems with the positive real (1, 1)-block sub-matrix. By a careful analysis of the spectral properties of the corresponding iteration matrix, we investigate the semi-convergence property of the GSS iteration method, give the sharper bounds of the eigenvalues for the GSS iteration method and propose the inexact GSS iteration method, also. Numerical experiments are given to show the correctness of the theoretical analysis and the feasibility of the GSS preconditioner with appropriate parameters.

Authors:
 [1];  [2]
  1. Chongqing University of Technology, School of Science (China)
  2. University of Electronic Science and Technology of China, School of Mathematical Sciences (China)
Publication Date:
OSTI Identifier:
22769367
Resource Type:
Journal Article
Journal Name:
Computational and Applied Mathematics
Additional Journal Information:
Journal Volume: 37; Journal Issue: 1; Other Information: Copyright (c) 2018 SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0101-8205
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; CONVERGENCE; EIGENVALUES; MATRICES

Citation Formats

Huang, Zhuo-Hong, and Huang, Ting-Zhu. On semi-convergence and inexact iteration of the GSS iteration method for nonsymmetric singular saddle point problems. United States: N. p., 2018. Web. doi:10.1007/S40314-016-0374-0.
Huang, Zhuo-Hong, & Huang, Ting-Zhu. On semi-convergence and inexact iteration of the GSS iteration method for nonsymmetric singular saddle point problems. United States. doi:10.1007/S40314-016-0374-0.
Huang, Zhuo-Hong, and Huang, Ting-Zhu. Thu . "On semi-convergence and inexact iteration of the GSS iteration method for nonsymmetric singular saddle point problems". United States. doi:10.1007/S40314-016-0374-0.
@article{osti_22769367,
title = {On semi-convergence and inexact iteration of the GSS iteration method for nonsymmetric singular saddle point problems},
author = {Huang, Zhuo-Hong and Huang, Ting-Zhu},
abstractNote = {In this paper, the generalized shift-splitting (GSS) iteration method is used to solve nonsymmetric singular saddle point systems with the positive real (1, 1)-block sub-matrix. By a careful analysis of the spectral properties of the corresponding iteration matrix, we investigate the semi-convergence property of the GSS iteration method, give the sharper bounds of the eigenvalues for the GSS iteration method and propose the inexact GSS iteration method, also. Numerical experiments are given to show the correctness of the theoretical analysis and the feasibility of the GSS preconditioner with appropriate parameters.},
doi = {10.1007/S40314-016-0374-0},
journal = {Computational and Applied Mathematics},
issn = {0101-8205},
number = 1,
volume = 37,
place = {United States},
year = {2018},
month = {3}
}