On diagonal and off-diagonal splitting-based iteration method to solve absolute value equations

Abstract

Lately, M. Dehghan et al. suggested a two-step iterative method for solving linear problems based on diagonal splitting and off-diagonal splitting (DOS) [Filomat 31:5 (2017) 1441--1452]. In this study, a two-step nonlinear DOS-like iteration method for solving absolute value equations is presented based on the DOS technique. Two linear subsystems need to be solved using the diagonal and lower triangular coefficient matrices in every iteration of the proposed approach. The convergence characteristics of the nonlinear DOS-like iteration technique are investigated under certain circumstances. Several examples are given to demonstrate the efficacy of the method.