论文标题
一般绝对值方程的误差和扰动边界
The error and perturbation bounds of the general absolute value equations
论文作者
论文摘要
据我们所知，未讨论一般绝对值方程的错误和扰动范围。为了通过引入一类绝对价值函数来填补本研究空白，我们研究了两种类型的一般绝对值方程（AVES）的误差和扰动界：$ ax-b | x | = b $和$ ax- | bx- | bx | = b $。提供了上述两种绝对值方程的一些有用的误差界和扰动范围。在不限制矩阵类型的情况下，给出了上述上限的一些可计算估计。通过应用绝对值方程，提供了一种新方法，用于（Siam J. Optim。，18（2007），第1250-1265页）中线性互补问题（LCP）的某些扰动范围。给出了来自LCP的Aves的一些数值示例，以显示扰动边界的可行性。
To our knowledge, the error and perturbation bounds of the general absolute value equations 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 and perturbation bounds of two types of the general absolute value equations (AVEs): $Ax-B|x|=b$ and $Ax-|Bx|=b$. Some useful error bounds and perturbation bounds of the above two types of absolute value equations are provided. Without limiting the matrix type, some computable estimates for the above upper bounds are given. By applying the absolute value equations, a new approach for some existing perturbation bounds of the linear complementarity problem (LCP) in (SIAM J. Optim., 18 (2007), pp. 1250-1265) is provided. Some numerical examples for the AVEs from the LCP are given to show the feasibility of the perturbation bounds.
