On SOR-like iteration methods for solving weakly nonlinear systems. (2nd January 2022)

• Record Type: Journal Article
• Authors: Ke, Yifen; Ma, Changfeng
• Is Part Of: Optimization methods and software. Volume 37:Number 1(2022)
• Page Start: 320
• Page End: 337
• Publication Date: 2022-01-02
• Subjects: Weakly nonlinear equation -- matrix splitting -- SOR -- convergence theory -- nonlinear convection-diffusion equation -- linear complementarity problem; 65H10 -- 65F10; Mathematical optimization -- Periodicals; Algorithms -- Periodicals; 519.7
• DOI: 10.1080/10556788.2020.1755861
• Languages: English
• ISSNs: 1055-6788

Abstract

ABSTRACT: 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.