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Neural network based on systematically generated smoothing functions for absolute value equation

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Abstract

In this paper, we summarize several systematic ways of constructing smoothing functions and illustrate eight smoothing functions accordingly. Then, based on these systematically generated smoothing functions, a unified neural network model is proposed for solving absolute value equation. The issues regarding the equilibrium point, the trajectory, and the stability properties of the neural network are addressed. Moreover, numerical experiments with comparison are presented, which suggests what kind of smoothing functions work well along with the neural network approach.

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Authors and Affiliations

  1. College of Mathematical Science, Inner Mongolia Normal University, Hohhot, 010022, Inner Mongolia, People’s Republic of China

    B. Saheya

  2. Department of Mathematics, National Taiwan Normal University, Taipei, 11677, Taiwan

    Chieu Thanh Nguyen & Jein-Shan Chen

Authors
  1. B. Saheya
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  2. Chieu Thanh Nguyen
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  3. Jein-Shan Chen
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Correspondence to Jein-Shan Chen.

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B. Saheya: The author’s work is supported by National Key R&D Program of China (Award No.: 2017YFC1405605) and Foundation of Inner Mongolia Normal University (Award No.: 2017YJRC003)

J.-S. Chen: The author’s work is supported by Ministry of Science and Technology, Taiwan.

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Saheya, B., Nguyen, C.T. & Chen, JS. Neural network based on systematically generated smoothing functions for absolute value equation. J. Appl. Math. Comput. 61, 533–558 (2019). https://doi.org/10.1007/s12190-019-01262-1

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  • DOI: https://doi.org/10.1007/s12190-019-01262-1

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