Journal
LINEAR ALGEBRA AND ITS APPLICATIONS
Volume 419, Issue 2-3, Pages 359-367Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.laa.2006.05.004
Keywords
absolute value equations; linear complementarity problems
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We investigate existence and nonexistence of solutions for NP-hard equations involving absolute values of variables: Ax - vertical bar x vertical bar = b, where A is an arbitrary n x n real matrix. By utilizing an equivalence relation to the linear complementarity problem (LCP) we give existence results for this class of absolute value equations (AVEs) as well as a method of solution for special cases. We also give nonexistence results for our AVE using theorems of the alternative and other arguments. (c) 2006 Elsevier Inc. All rights reserved.
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