Shouheng Tuo
Shaanxi University of Technology

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Quasi-Newton Method for Absolute Value Equation Based on Upper Uniform Smoothing Approximation Longquan Yong; Shouheng Tuo
TELKOMNIKA (Telecommunication Computing Electronics and Control) Vol 14, No 3: September 2016
Publisher : Universitas Ahmad Dahlan

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.12928/telkomnika.v14i3.3785

Abstract

In this paper, an upper uniform smooth approximation function of absolute value function is proposed, and some properties of uniform smooth approximation function are studied. Then, absolute value equation (AVE), Ax - |x| = b, where A is a square matrix whose singular values exceed one, is transformed into smooth optimization problem by using the upper uniform smooth approximation function, and solved by quasi-Newton method. Numerical results in solving given AVE problems demonstrated that our algorithm is valid and superior to lower uniform smooth approximation function.