Some notes on the solvability conditions for absolute value equations
Abstract: Motivated by recently published papers, we discuss the problem of solving absolute value equations of the form \(Ax+|x|=b\). Specifically, we show the equivalence of two sufficient conditions for the unsolvability of such equations which are based on linear programming. Furthermore, we prove that two generalizations of sufficient conditions for unique solvability do not extend the class at all, that is, they are equivalent to the original formulations. The conditions based on M-matrices and H-matrices also turn out to be special cases of the known statements. Eventually, we also point out two incorrect statements, and for one of them, we propose some corrected reformulations.
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