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A Class of Preconditioned TGHSS-Based Iteration Methods for Weakly Nonlinear Systems

Part of: Numerical linear algebra

Published online by Cambridge University Press:  19 October 2016

Min-Li Zeng  and
Guo-Feng Zhang
Min-Li Zeng*
Affiliation:
School of Mathematics, Putian University, Putian 351100, China
Guo-Feng Zhang*
Affiliation:
School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, China
*
*Corresponding author. Email addresses:zengml12@lzu.edu.cn (M.-L. Zeng), gf_zhang@lzu.edu.cn (G.-F. Zhang)
*Corresponding author. Email addresses:zengml12@lzu.edu.cn (M.-L. Zeng), gf_zhang@lzu.edu.cn (G.-F. Zhang)

Abstract

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In this paper, we first construct a preconditioned two-parameter generalized Hermitian and skew-Hermitian splitting (PTGHSS) iteration method based on the two-parameter generalized Hermitian and skew-Hermitian splitting (TGHSS) iteration method for non-Hermitian positive definite linear systems. Then a class of PTGHSS-based iteration methods are proposed for solving weakly nonlinear systems based on separable property of the linear and nonlinear terms. The conditions for guaranteeing the local convergence are studied and the quasi-optimal iterative parameters are derived. Numerical experiments are implemented to show that the new methods are feasible and effective for large scale systems of weakly nonlinear systems.

Keywords

System of weakly nonlinear equationsGHSS iteration methodlocal convergenceinner iterationouter iteration

MSC classification

Secondary: 65F10: Iterative methods for linear systems 65F50: Sparse matrices

Information

Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 6 , Issue 4 , November 2016 , pp. 367 - 383
Copyright
Copyright © Global-Science Press 2016 

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