A two-step iterative fixed-point method for new general absolute value equations

Abstract

In this work, we have studied a class of new general absolute value equation (NGAVE) of type: $ Ax-\left\vert Bx\right\vert =b$, ($A$, $B\in \mathbb{R}^{n\times n} $, $b\in \mathbb{R}^{n}$) are given. Some weaker sufficient conditions for the unique solvability of the NGAVE are also obtained. For its numerical solution, a two-steps Picard's fixed-point iterative method is proposed. Moreover, we have proved under an appropriate assumption that the proposed algorithm is well-defined and converges globally linearly to the unique solution of NGAVE. Finally, we present a various set of numerical results to confirm the efficiency of our proposed approach.