Matrix splitting iteration method for generalized absolute value matrix equation

Abstract

In this dissertation, we study generalized absolute value matrix equations of the form AX−B|X|=C where A, B, C, X ∈ R^(n×n) ,which are non linear due to the presence of the absolute value operator. Using the matrix splitting technique, we propose a Newton-based iterative method as well as a relaxeds versions. This general framework includes classical methods such as Picard’s method and the modified Newton method. We establish sufficient conditions and analyze the convergence properties, proving global linear convergence under suitable assumptions. Numerical experiments carried out using MATLAB confirm the effectiveness of the proposed methods for both symmetric and non-symmetric matrices