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
收藏
页码：320 / 337
页数：18
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