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In this paper, inspired by in the pervious published work in [Math. Program.,198 (2023), pp. 85-113] by Zamani and Hlad\'{\i}k, we focus on the error andperturbation bounds for the general absolute value equations because so far, toour knowledge, the error and perturbation bounds for the general absolute valueequations are not discussed. In order to fill in this study gap, in this paper,by introducing a class of absolute value functions, we study the error boundsand perturbation bounds for two types of absolute value equations (AVEs):$Ax-B|x|=b$ and $Ax-|Bx|=b$. Some useful error bounds and perturbation boundsfor the above two types of absolute value equations are presented. By applyingthe absolute value equations, we also obtain the error and perturbation boundsfor the horizontal linear complementarity problem (HLCP). In addition, a newperturbation bound for the LCP without constraint conditions is given as well,which are weaker than the presented work in [SIAM J. Optim., 2007, 18:1250-1265] in a way. Besides, without limiting the matrix type, some computableestimates for the above upper bounds are given, which are sharper than someexisting results under certain conditions. Some numerical examples for the AVEsfrom the LCP are given to show the feasibility of the perturbation bounds.

The error and perturbation bounds for the absolute value equations with some applications