In this paper, by introducing a class of absolute value functions, we study the error bounds and perturbation bounds of two types of absolute value equations (AVEs): Ax -B|x|= b and Ax -|Bx|= b. Some useful error bounds and perturbation bounds for the above two types of absolute value equations are presented. By applying the absolute value equations, we obtain some useful error bounds and perturbation bounds for the horizontal linear complementarity problem (HLCP). Incidentally, two new error bounds for linear complementarity problem (LCP) are given, coincidentally, which are equal to the existing result. Without constraint conditions, a new perturbation bound for the LCP is given as well. Besides, without limiting the matrix type, some computable estimates for the above upper bounds are given, which are sharper than some existing results under certain conditions. Some numerical examples for the AVEs from the LCP are given to show the feasibility of the perturbation bounds.

翻译：在本文中,通过引入绝对值函数的类别,我们研究了两种绝对值方程式(AVes)的错误界限和扰动界限:Ax-B ⁇ x ⁇ b和Ax- ⁇ Bx ⁇ b。为以上两种绝对值方程式提供了一些有用的错误界限和扰动界限。通过应用绝对值方程式,我们获得了一些有用的错误界限和对水平线性互补问题(CPL)的扰动界限。顺便提一下,对线性互补问题(LCP)给出了两个新的错误界限,这与现有结果相等。此外,在没有限制条件的情况下,还给出了受LCP约束的新的扰动界限。此外,在不限制矩阵类型的情况下,还给出了以上上方方方程式的一些可比较的估计数,这些估计数比某些条件下的某些现有结果要清晰。一些LCPAVes的数字示例显示了扰动界限的可行性。