A constructive approach for finding arbitrary roots of polynomials by neural networks

IEEE Transactions on Neural Networks
De-Shuang Huang

Abstract

This paper proposes a constructive approach for finding arbitrary (real or complex) roots of arbitrary (real or complex) polynomials by multilayer perceptron network (MLPN) using constrained learning algorithm (CLA), which encodes the a priori information of constraint relations between root moments and coefficients of a polynomial into the usual BP algorithm (BPA). Moreover, the root moment method (RMM) is also simplified into a recursive version so that the computational complexity can be further decreased, which leads the roots of those higher order polynomials to be readily found. In addition, an adaptive learning parameter with the CLA is also proposed in this paper; an initial weight selection method is also given. Finally, several experimental results show that our proposed neural connectionism approaches, with respect to the nonneural ones, are more efficient and feasible in finding the arbitrary roots of arbitrary polynomials.

References

Jan 1, 1995·IEEE Transactions on Neural Networks·D A Karras, S J Perantonis

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Citations

Jul 17, 2013·BMC Bioinformatics·Ben NiuLi Li
Feb 19, 2013·PloS One·Zhan-Li SunChun-Hou Zheng
Feb 14, 2008·IEEE Transactions on Neural Networks·Z Wang, B S Peterson
Jun 9, 2005·IEEE Transactions on Neural Networks·De-Shuang HuangZheru Chi
Aug 27, 2005·IEEE Transactions on Neural Networks·Qingshan LiuYoushen Xia
Sep 6, 2005·Neural Networks : the Official Journal of the International Neural Network Society·Hongyong Zhao, Jinde Cao
Jan 21, 2017·Computational Intelligence and Neuroscience·Haizhou WuMohamed Abdel Basset
Aug 24, 2018·International Journal of Molecular Sciences·Yumeng LiuBin Liu
Jun 23, 2016·Journal of the Air & Waste Management Association·Qian DiJoel Schwartz
Jan 5, 2021·Neurocomputing·Xiang YuYu-Dong Zhang
Jul 10, 2021·Scientific Reports·Abdulkadir Tasdelen, Baha Sen
Jul 13, 2021·Multimedia Tools and Applications·Chih-Yu HsuYu Qiao

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