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

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Author(s)

Detail(s)

Original languageEnglish
Pages (from-to)443-451
Journal / PublicationPhysics Letters, Section A: General, Atomic and Solid State Physics
Volume309
Issue number5-6
Publication statusPublished - 31 Mar 2003

Abstract

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. © 2003 Elsevier Science B.V. All rights reserved.

Research Area(s)

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

Citation Format(s)

Dilation method for finding close roots of polynomials based on constrained learning neural networks. / Huang, De-Shuang; Ip, Horace H.S.; Chi, Zheru et al.

In: Physics Letters, Section A: General, Atomic and Solid State Physics, Vol. 309, No. 5-6, 31.03.2003, p. 443-451.

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review