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Some techniques for solving absolute value equations
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DOI：10.1016/j.amc.2015.06.072.png)
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Abstract
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In this paper, we introduce and analyze two new methods for solving the NP-hard absolute value equations (AVE) Ax - vertical bar x vertical bar = b, where A is an arbitrary n x n real matrix and b is an element of R-n, in the case, singular value of A exceeds 1. The comparison with other known methods is carried to show the effectiveness of the proposed methods for a variety of randomly generated problems. The ideas and techniques of this paper may stimulate further research. (C) 2015 Elsevier Inc. All rights reserved.
Keywords:
Absolulte value equation
Generalized Newton method
Homotopy perturbation method
The successive linearization algorithm
Singular values
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