A globally and quadratically convergent method for absolute value equations

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Article ID:	iaor20111342
Volume:	48
Issue:	1
Start Page Number:	45
End Page Number:	58
Publication Date:	Jan 2011
Journal:	Computational Optimization and Applications
Authors:	Zhou Guanglu, Qu Biao, Caccetta Louis
Keywords:	Newton method

Abstract:

We investigate the NP‐hard absolute value equation (AVE) Ax-|x|=b, where A is an arbitrary n×n real matrix. In this paper, we propose a smoothing Newton method for the AVE. When the singular values of A exceed 1, we show that this proposed method is globally convergent and the convergence rate is quadratic. Preliminary numerical results show that this method is promising.

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