Zeroing polynomials using modified constrained neural network approach

De Shuang Huang, Horace H.S. Ip, Ken Chee Keung Law, Zheru Chi

Research output: Journal article publicationJournal articleAcademic researchpeer-review

93 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)721-732
Number of pages12
JournalIEEE Transactions on Neural Networks
Issue number3
Publication statusPublished - 1 May 2005


  • Backpropagation networks (BPNs)
  • Computational complexity
  • Laguerre's and Muller's methods
  • Modified constrained learning algorithm (MCLA)
  • Perturbation
  • Polynomials
  • Root finder

ASJC Scopus subject areas

  • Software
  • Computer Science Applications
  • Computer Networks and Communications
  • Artificial Intelligence


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