Dilation method for finding close roots of polynomials based on constrained learning neural networks

De Shuang Huang, Horace H.S. Ip, Zheru Chi, H. S. Wong

Research output: Journal article publicationJournal articleAcademic researchpeer-review

48 Citations (Scopus)


In finding roots of polynomials, often two or more roots that are close together in solution space are very difficult to be resolved by a root-finder. To solve this problem, this Letter proposes a dilation method to transform the positions of roots in space so that all roots in space are pulled further apart. As a result, those close (including complex) roots can be readily resolved efficiently by a root-finder. In addition, in this Letter a complex version of constrained learning algorithm is derived. Moreover, our previously proposing feedforward neural network (FNN) root-finder is adopted to address the root finding issue. Finally, some satisfactory results that support our approach are presented.
Original languageEnglish
Pages (from-to)443-451
Number of pages9
JournalPhysics Letters, Section A: General, Atomic and Solid State Physics
Issue number5-6
Publication statusPublished - 31 Mar 2003


  • Close roots
  • Complex constrained learning algorithm
  • Dilation
  • Feedforward neural networks
  • Polynomials
  • Root-finder

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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