On the unique solution of the generalized absolute value equation

05/07/2020

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by   Shi-Liang Wu, et al.

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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∈R^n× 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∈R^n× 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.