New smoothing function for solving absolute value equations

Abstract

In this paper, we use a smoothing-type algorithm in this paper to solve the AVE, which stands for the absolute value equation [Formula: see text], where [Formula: see text] is an arbitrary [Formula: see text] real matrix and [Formula: see text]. We reformulate AVE as a system of smooth equations and propose two new smoothing functions. We prove that the algorithm is well-defined when the singular value of [Formula: see text] exceeds one, and under the same assumption, the algorithm is convergent. We show the algorithm’s effectiveness with these two functions and compare it with some previously known functions.