The error and perturbation bounds of the general absolute value equations

2022/07/03 by Shi-Liang Wu, Wu, Shi-Liang, Li, Cui-Xia · 1 citation
Engineering · #Advanced Numerical Analysis Techniques

paper · pdf · doi:10.48550/arxiv.2207.00954

Abstract

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.

Cited by

• Randomized iterative methods with Polyak step-size for solving generalized absolute value equations

Related

• Error bounds and a condition number for the absolute value equations
• An Overview of Absolute Value Equations: From Theory to Solution Methods and Challenges
• Sign controlled solvers for the absolute value equation with an application to support vector machines
• Error Bound for the Linear Complementarity Problem using Plus Function
• Properties of the solution set of absolute value equations and the related matrix classes