A new class of fixed point methods for solving absolute value equations

Abstract

This paper deals with developing a new class of fixed point iterative methods for solving the absolute value equation (AVE) of the form $Ax − |x| = b$. In theory, exploiting two distinct splittings of the matrix $A$, the approach is constructed by formulating a block system of nonlinear equations. Sufficient conditions are provided for (unique) solvability of the underlying block system, ensuring that any solution to this system also yields a solution to the given AVE. We further develop a Kellogg-type class of iterative methods for solving the considered AVE and establish the convergence properties of the proposed approach. Additionally, we disclose numerical experiments that illustrate superiority of the proposed class of iterative methods over two recently proposed methods in the literature.