The solution of a type of absolute value equations using two new matrix splitting iterative techniques

Abstract

Finding the solution of an absolute value vector equation (AVE) of the form $$ Ax-\vert x\vert= b $$ is an important subject in scientific computing, operations research, engineering, management science, and economic applications. This paper proposes two new iterative techniques to solve such AVEs. Both techniques are based on a decomposition of the coefficient matrix and a fixed-point principle. The convergence of the proposed techniques under appropriate assumptions is examined. We present results of numerical simulations to verify our theoretical findings and demonstrate the efficiency of our techniques.