Iterative schemes induced by block splittings for solving absolute value equations

Abstract

In this paper, we develop the idea of constructing iterative methods based on block splittings (BBS) to solve absolute value equations. The class of BBS methods incorporates the well-known Picard iterative method as a special case. Convergence properties of mentioned schemes are proved under some sufficient conditions. Numerical experiments are examined to compare the performance of the iterative schemes of BBS-type with some of existing approaches in the literature such as generalized Newton and Picard(-HSS) iterative methods.