A new partitioning neural network model for recursively finding arbitrary roots of higher order arbitrary polynomials

De Shuang Huang, H. S.Ip Horace, C. K. Law Ken, Zheru Chi, H. S. Wong

Research output: Journal article publicationJournal articleAcademic researchpeer-review

17 Citations (Scopus)

Abstract

A new partitioning feedforward neural network (FNN) root-finder model for recursively finding the arbitrary (including complex) roots of higher order arbitrary polynomials is proposed in this paper. Moreover, an efficient complex version of constrained learning algorithm (CLA), which incorporates the a priori information, i.e., the constrained relation between the original polynomial coefficients and the remaining polynomial coefficients plus the partitioned roots out from the original polynomial, is constructed to train the corresponding partitioning neural root-finder network for finding the arbitrary roots of arbitrary polynomials. Finally, the experimental results are given to show the efficiency and effectiveness of our proposed neural model with respect to traditional non-neural root-finders.
Original languageEnglish
Pages (from-to)1183-1200
Number of pages18
JournalApplied Mathematics and Computation
Volume162
Issue number3
DOIs
Publication statusPublished - 25 Mar 2005

Keywords

  • Complex constrained learning algorithm
  • Feedforward neural network
  • Jenkins-Traub method
  • Laguerre method
  • Muller method
  • Partitioning
  • Polynomial
  • Roots-finder

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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