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Title: The generalized Uzawa-SHSS method for non-Hermitian saddle-point problems

Abstract

Recently, Li and Wu (2015) proposed the single-step Hermitian and skew-Hermitian splitting (SHSS) method for solving the non-Hermitian positive definite linear systems. Based on the single-step Hermitian and skew-Hermitian splitting of the (1,1) part of the saddle-point coefficient matrix, a new Uzawa-type method is proposed for solving a class of saddle-point problems with non-Hermitian positive definite (1,1) parts. Convergence (Semi-convergence) properties of this new method for nonsingular (singular) are derived under suitable conditions. Numerical examples are implemented to confirm the theoretical results and verify that this new method is more feasibility and robustness than the new HSS-like (NHSS-like), the Uzawa-HSS and the parameterized Uzawa-skew-Hermitian triangular splitting (PU-STS) methods for solving both the nonsingular and the singular saddle-point problems with non-Hermitian positive definite and Hermitian dominant (1,1) parts.

Authors:
; ; ;  [1]
  1. Northwestern Polytechnical University, Department of Applied Mathematics, School of Science (China)
Publication Date:
OSTI Identifier:
22769355
Resource Type:
Journal Article
Journal Name:
Computational and Applied Mathematics
Additional Journal Information:
Journal Volume: 37; Journal Issue: 2; 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; MATRICES; SADDLE-POINT METHOD

Citation Formats

Huang, Zhengge, Wang, Ligong, Xu, Zhong, and Cui, Jingjing. The generalized Uzawa-SHSS method for non-Hermitian saddle-point problems. United States: N. p., 2018. Web. doi:10.1007/S40314-016-0390-0.
Huang, Zhengge, Wang, Ligong, Xu, Zhong, & Cui, Jingjing. The generalized Uzawa-SHSS method for non-Hermitian saddle-point problems. United States. doi:10.1007/S40314-016-0390-0.
Huang, Zhengge, Wang, Ligong, Xu, Zhong, and Cui, Jingjing. Tue . "The generalized Uzawa-SHSS method for non-Hermitian saddle-point problems". United States. doi:10.1007/S40314-016-0390-0.
@article{osti_22769355,
title = {The generalized Uzawa-SHSS method for non-Hermitian saddle-point problems},
author = {Huang, Zhengge and Wang, Ligong and Xu, Zhong and Cui, Jingjing},
abstractNote = {Recently, Li and Wu (2015) proposed the single-step Hermitian and skew-Hermitian splitting (SHSS) method for solving the non-Hermitian positive definite linear systems. Based on the single-step Hermitian and skew-Hermitian splitting of the (1,1) part of the saddle-point coefficient matrix, a new Uzawa-type method is proposed for solving a class of saddle-point problems with non-Hermitian positive definite (1,1) parts. Convergence (Semi-convergence) properties of this new method for nonsingular (singular) are derived under suitable conditions. Numerical examples are implemented to confirm the theoretical results and verify that this new method is more feasibility and robustness than the new HSS-like (NHSS-like), the Uzawa-HSS and the parameterized Uzawa-skew-Hermitian triangular splitting (PU-STS) methods for solving both the nonsingular and the singular saddle-point problems with non-Hermitian positive definite and Hermitian dominant (1,1) parts.},
doi = {10.1007/S40314-016-0390-0},
journal = {Computational and Applied Mathematics},
issn = {0101-8205},
number = 2,
volume = 37,
place = {United States},
year = {2018},
month = {5}
}