On SOR-like iteration methods for solving weakly nonlinear systems

被引：6

作者：

Ke, Yifen ^{[1
,2
]}

Ma, Changfeng ^{[1
,2
]}

机构：

[1] Fujian Normal Univ, Coll Math & Informat, Fuzhou 350117, Peoples R China

[2] Fujian Normal Univ, FJKLMAA, Fuzhou 350117, Peoples R China

来源：

OPTIMIZATION METHODS & SOFTWARE | 2022年 / 37卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Weakly nonlinear equation; matrix splitting; SOR; convergence theory; nonlinear convection-diffusion equation; linear complementarity problem; CONJUGATE-GRADIENT; NEWTON METHOD; CONVERGENCE;

D O I：

10.1080/10556788.2020.1755861

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

In this paper, we introduce a class of SOR-like iteration methods for solving the systems of the weakly nonlinear equation, which is by reformulating equivalently the weakly nonlinear equation as a two-by-two block nonlinear equation. Two types of the global convergence theorems are given under suitable choices of the involved splitting matrix and parameter. Numerical results for the three-dimensional nonlinear convection-diffusion equation and the linear complementarity problem show that the proposed iteration methods are feasible and efficient for solving the weakly nonlinear equations.

引用

页码：320 / 337

页数：18

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