On the unique solution of the generalized absolute value equation


Abstract in English

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 $A, Bin mathbb{R}^{ntimes n}$ from the optimization field are first presented, which cover the fundamental theorem for the unique solution of the linear system $Ax=b$ with $Ain mathbb{R}^{ntimes n}$. Not only that, some new sufficient conditions for the unique solution of the GAVE are obtained, which are weaker than the previous published works.

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