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The error and perturbation bounds for the absolute value equations with some applications
To our knowledge, so far, the error and perturbation bounds for 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 bounds and perturbation bounds for 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 also obtain the error and
perturbation bounds for the horizontal linear complementarity problem (HLCP).
In addition, a new perturbation 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
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
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