A cluster-based technique for solving the GAVE

Abstract

Abstract Generalized absolute value equation (abbreviated as GAVE) has wide applications in scientific computing and engineering. In this paper, we propose a cluster-based technique for solving the GAVE. First, the GAVE is shown to be equivalent to a linear equation which is related to the signs of the solution. In order to avoid the disadvantage of the existence of the sign index sets which is problem depended, by the framework of a fixed-point iteration, the analysis of the signs of the iteration vectors is given. Some necessary conditions of the nonzero and zero entries of the iteration vector are presented. Then, the signs of the solution of the GAVE can be partitioned by a clustering process. Numerical examples show that the proposed technique can work and significantly accelerate the computational efficiency comparing to some existing methods.