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Title: On LPMHSS-based iteration methods for a class of weakly nonlinear systems

Abstract

In this paper, for a class of the large sparse system of weakly nonlinear equations, combining separable property of the linear and nonlinear terms with the lopsided Hermitian and skew-Hermitian splitting (LHSS) of the coefficient matrix, the Picard-LPMHSS and nonlinear LPMHSS-like iteration methods are presented. Theoretical analysis shows that these methods are locally convergent under suitable conditions. Numerical results show that both Picard-LPMHSS and nonlinear LPMHSS-like iteration methods are feasible and effective for the large-scale system of weakly nonlinear equations.

Authors:
;  [1]
  1. Anyang Normal University, School of Mathematics and Statistics (China)
Publication Date:
OSTI Identifier:
22769351
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; EQUATIONS; MATRICES; NONLINEAR PROBLEMS

Citation Formats

Li, Cui-Xia, and Wu, Shi-Liang. On LPMHSS-based iteration methods for a class of weakly nonlinear systems. United States: N. p., 2018. Web. doi:10.1007/S40314-016-0395-8.
Li, Cui-Xia, & Wu, Shi-Liang. On LPMHSS-based iteration methods for a class of weakly nonlinear systems. United States. doi:10.1007/S40314-016-0395-8.
Li, Cui-Xia, and Wu, Shi-Liang. Tue . "On LPMHSS-based iteration methods for a class of weakly nonlinear systems". United States. doi:10.1007/S40314-016-0395-8.
@article{osti_22769351,
title = {On LPMHSS-based iteration methods for a class of weakly nonlinear systems},
author = {Li, Cui-Xia and Wu, Shi-Liang},
abstractNote = {In this paper, for a class of the large sparse system of weakly nonlinear equations, combining separable property of the linear and nonlinear terms with the lopsided Hermitian and skew-Hermitian splitting (LHSS) of the coefficient matrix, the Picard-LPMHSS and nonlinear LPMHSS-like iteration methods are presented. Theoretical analysis shows that these methods are locally convergent under suitable conditions. Numerical results show that both Picard-LPMHSS and nonlinear LPMHSS-like iteration methods are feasible and effective for the large-scale system of weakly nonlinear equations.},
doi = {10.1007/S40314-016-0395-8},
journal = {Computational and Applied Mathematics},
issn = {0101-8205},
number = 2,
volume = 37,
place = {United States},
year = {2018},
month = {5}
}