DPMHSS-based iteration methods for solving weakly nonlinear systems with complex coefficient matrices

Min-Hong Chen; Wei Dou; Qing Biao Wu

doi:10.1016/j.apnum.2019.07.018

DPMHSS-based iteration methods for solving weakly nonlinear systems with complex coefficient matrices

Min-Hong Chen
, Wei Dou
, Qing Biao Wu (Lead / Corresponding author)

Mathematics

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

23 Downloads (Pure)

Abstract

In this paper, we aim at giving efficient iterative methods for solving large sparse weakly nonlinear systems with complex symmetric coefficient matrices. Based on the separable property of the linear and nonlinear terms, and by combining with the double-parameter preconditioned MHSS (DPMHSS) method for linear systems, we propose the Picard-DPMHSS and nonlinear DPMHSS-like methods. Under suitable conditions, we establish convergence theorems for the Picard-DPMHSS and nonlinear DPMHSS-like methods. Numerical implementations show that both Picard-DPMHSS and nonlinear DPMHSS-like iteration methods are effective solvers for large sparse weakly nonlinear systems.

Original language	English
Pages (from-to)	328-341
Number of pages	14
Journal	Applied Numerical Mathematics
Volume	146
Early online date	19 Jul 2019
DOIs	https://doi.org/10.1016/j.apnum.2019.07.018
Publication status	Published - Dec 2019

Keywords

Convergence theorem
DPMHSS iteration method
Inner-outer iteration scheme
Nonlinear iteration scheme
Weakly nonlinear system

ASJC Scopus subject areas

Numerical Analysis
Computational Mathematics
Applied Mathematics

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Author Accepted ManuscriptAccepted author manuscript, 142 KBLicence: CC BY-NC-ND

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title = "DPMHSS-based iteration methods for solving weakly nonlinear systems with complex coefficient matrices",

abstract = "In this paper, we aim at giving efficient iterative methods for solving large sparse weakly nonlinear systems with complex symmetric coefficient matrices. Based on the separable property of the linear and nonlinear terms, and by combining with the double-parameter preconditioned MHSS (DPMHSS) method for linear systems, we propose the Picard-DPMHSS and nonlinear DPMHSS-like methods. Under suitable conditions, we establish convergence theorems for the Picard-DPMHSS and nonlinear DPMHSS-like methods. Numerical implementations show that both Picard-DPMHSS and nonlinear DPMHSS-like iteration methods are effective solvers for large sparse weakly nonlinear systems.",

keywords = "Convergence theorem, DPMHSS iteration method, Inner-outer iteration scheme, Nonlinear iteration scheme, Weakly nonlinear system",

author = "Min-Hong Chen and Wei Dou and Wu, \{Qing Biao\}",

note = "Publisher Copyright: {\textcopyright} 2019 IMACS",

year = "2019",

month = dec,

doi = "10.1016/j.apnum.2019.07.018",

language = "English",

volume = "146",

pages = "328--341",

journal = "Applied Numerical Mathematics",

issn = "0168-9274",

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TY - JOUR

T1 - DPMHSS-based iteration methods for solving weakly nonlinear systems with complex coefficient matrices

AU - Chen, Min-Hong

AU - Dou, Wei

AU - Wu, Qing Biao

PY - 2019/12

Y1 - 2019/12

N2 - In this paper, we aim at giving efficient iterative methods for solving large sparse weakly nonlinear systems with complex symmetric coefficient matrices. Based on the separable property of the linear and nonlinear terms, and by combining with the double-parameter preconditioned MHSS (DPMHSS) method for linear systems, we propose the Picard-DPMHSS and nonlinear DPMHSS-like methods. Under suitable conditions, we establish convergence theorems for the Picard-DPMHSS and nonlinear DPMHSS-like methods. Numerical implementations show that both Picard-DPMHSS and nonlinear DPMHSS-like iteration methods are effective solvers for large sparse weakly nonlinear systems.

AB - In this paper, we aim at giving efficient iterative methods for solving large sparse weakly nonlinear systems with complex symmetric coefficient matrices. Based on the separable property of the linear and nonlinear terms, and by combining with the double-parameter preconditioned MHSS (DPMHSS) method for linear systems, we propose the Picard-DPMHSS and nonlinear DPMHSS-like methods. Under suitable conditions, we establish convergence theorems for the Picard-DPMHSS and nonlinear DPMHSS-like methods. Numerical implementations show that both Picard-DPMHSS and nonlinear DPMHSS-like iteration methods are effective solvers for large sparse weakly nonlinear systems.

KW - Convergence theorem

KW - DPMHSS iteration method

KW - Inner-outer iteration scheme

KW - Nonlinear iteration scheme

KW - Weakly nonlinear system

UR - https://www.scopus.com/pages/publications/85069916555

U2 - 10.1016/j.apnum.2019.07.018

DO - 10.1016/j.apnum.2019.07.018

M3 - Article

AN - SCOPUS:85069916555

SN - 0168-9274

VL - 146

SP - 328

EP - 341

JO - Applied Numerical Mathematics

JF - Applied Numerical Mathematics

ER -

DPMHSS-based iteration methods for solving weakly nonlinear systems with complex coefficient matrices

Abstract

Keywords

ASJC Scopus subject areas

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