On the unique solution of the generalized absolute value equation

Abstract

In this paper, some useful necessary and sufficient conditions for the unique solution of the generalized absolute value equation (GAVE) $Ax-B|x|=b$ with $A,B\in {\mathbb{R}}^{n\times n}$ from the optimization field are first presented, which cover the fundamental theorem for the unique solution of the linear system $Ax=b$ with $A\in {\mathbb{R}}^{n\times n}$. Not only that, some new sufficient conditions for the unique solution of the GAVE are obtained, which are weaker than the previous published works.

8 pages, submitted