Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/31960
Title: Zeroing polynomials using modified constrained neural network approach
Authors: Huang, DS
Ip, HHS
Law, KCK
Chi, Z 
Keywords: Backpropagation networks (BPNs)
Computational complexity
Laguerre's and Muller's methods
Modified constrained learning algorithm (MCLA)
Perturbation
Polynomials
Root finder
Issue Date: 2005
Publisher: Institute of Electrical and Electronics Engineers
Source: IEEE transactions on neural networks, 2005, v. 16, no. 3, p. 721-732 How to cite?
Journal: IEEE transactions on neural networks 
Abstract: This paper proposes new modified constrained learning neural root finders (NRFs) of polynomial constructed by backpropagation network (BPN). The technique is based on the relationships between the roots and the coefficients of polynomial as well as between the root moments and the coefficients of the polynomial. We investigated different resulting constrained learning algorithms (CLAs) based on the variants of the error cost functions (ECFs) in the constrained BPN and derived a new modified CLA (MCLA), and found that the computational complexities of the CLA and the MCLA based on the root-moment method (RMM) are the order of polynomial, and that the MCLA is simpler than the CLA. Further, we also discussed the effects of the different parameters with the CLA and the MCLA on the NRFs. In particular, considering the coefficients of the polynomials involved in practice to possibly be perturbed by noisy sources, thus, we also evaluated and discussed the effects of noises on the two NRFs. Finally, to demonstrate the advantage of our neural approaches over the nonneural ones, a series of simulating experiments are conducted.
URI: http://hdl.handle.net/10397/31960
ISSN: 1045-9227
DOI: 10.1109/TNN.2005.844912
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