Some techniques for solving absolute value equations

In this paper, we introduce and analyze two new methods for solving the NP-hard absolute value equations (AVE) Ax−|x|=b, where A is an arbitrary n × n real matrix and b ∈ Rn, in the case, singular value of A exceeds 1. The comparison with other known methods is carried to show the effectiveness of t...

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Bibliographic Details
Published in:Applied mathematics and computation Vol. 268; pp. 696 - 705
Main Authors: Moosaei, H., Ketabchi, S., Noor, M.A., Iqbal, J., Hooshyarbakhsh, V.
Format: Journal Article
Language:English
Published: Elsevier Inc 01.10.2015
Subjects:
Absolute value equation
Generalized Newton method
Homotopy perturbation method
Singular values
The successive linearization algorithm
Absolute value equation
90C33
Singular values
15A06
Homotopy perturbation method
65H10
Generalized Newton method
The successive linearization algorithm
ISSN:0096-3003, 1873-5649
Online Access:Get full text
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Summary:In this paper, we introduce and analyze two new methods for solving the NP-hard absolute value equations (AVE) Ax−|x|=b, where A is an arbitrary n × n real matrix and b ∈ Rn, 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.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2015.06.072