Two New Iteration Methods with Optimal Parameters for Solving Absolute Value Equations

Many problems in the fields of management science, operation research, and engineering can be solved using absolute value equations (AVEs). Recently, the generalized Gauss–Seidel (GGS) iteration technique has been developed (Edalatpour et al. [Appl. Math. Comput., 293:156–167, 2017]). This paper presents two new iteration methods that extend the GGS iteration technique with three additional parameters for solving AVEs. Moreover, we present the convergence results of these methods via some theorems. Numerical examples demonstrate the credibility of our methodologies. © 2022, The Author(s), under exclusive licence to Springer Nature India Private Limited.