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Approximation of algebraic and trigonometric polynomials by feedforward neural networks

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Abstract

This paper presents a function approximation to a general class of polynomials by using one-hidden-layer feedforward neural networks(FNNs). Both the approximations of algebraic polynomial and trigonometric polynomial functions are discussed in details. For algebraic polynomial functions, an one-hidden-layer FNN with chosen number of hidden-layer nodes and corresponding weights is established by a constructive method to approximate the polynomials to a remarkable high degree of accuracy. For trigonometric functions, an upper bound of approximation is therefore derived by the constructive FNNs. In addition, algorithmic examples are also included to confirm the accuracy performance of the constructive FNNs method. The results show that it improves efficiently the approximations of both algebraic polynomials and trigonometric polynomials. Consequently, the work is really of both theoretical and practical significance in constructing a one-hidden-layer FNNs for approximating the class of polynomials. The work also paves potentially the way for extending the neural networks to approximate a general class of complicated functions both in theory and practice.

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Acknowledgement

This work was supported by Natural Science Foundation of China (NOs.11001227, 60972155),the Key Project of Chinese Ministry of Education (No.108176), Natural Science Foundation Project of CQ CSTC(No.CSTC, 2009BB2306, CSTC2009BB2305), the Fundamental Research Funds for the Central Universities(No.XDJK2010B005, XDJK2010C023).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Southwest University, Chongqing, 400715, People’s Republic of China

    Jian-Jun Wang

  2. Institute for Information and System Science, Xi’an Jiaotong University, Xi’an, 710049, People’s Republic of China

    Jian-Jun Wang & Bai-Li Chen

  3. Department of Mechanical Engineering, Technology and Science Institute of Northern Taiwan, No. 2 Xue-Yuan Rd, Beitou, Taipei, 112, Taiwan

    Chan-Yun Yang

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  1. Jian-Jun Wang
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  2. Bai-Li Chen
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  3. Chan-Yun Yang
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Correspondence to Jian-Jun Wang.

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Wang, JJ., Chen, BL. & Yang, CY. Approximation of algebraic and trigonometric polynomials by feedforward neural networks. Neural Comput & Applic 21, 73–80 (2012). https://doi.org/10.1007/s00521-011-0617-3

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  • DOI: https://doi.org/10.1007/s00521-011-0617-3

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