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

doi:10.1016/S0375-9601(03)00216-0

Author(s)

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

Related Research Unit(s)

Detail(s)

Original language	English
Pages (from-to)	443-451
Journal / Publication	Physics Letters, Section A: General, Atomic and Solid State Physics
Volume	309
Issue number	5-6
Publication status	Published - 31 Mar 2003

Link(s)

DOI	DOI https://doi.org/10.1016/S0375-9601(03)00216-0 Final Published version
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Link to Scopus	https://www.scopus.com/record/display.uri?eid=2-s2.0-0037474728&origin=recordpage
Permanent Link	https://scholars.cityu.edu.hk/en/publications/publication(3c7753b6-c289-4858-a81b-b0ab6158880d).html

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)

[ RIS ] [ BibTeX ]

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 journal › peer-review

Huang, D-S, Ip, HHS, Chi, Z & Wong, HS 2003, 'Dilation method for finding close roots of polynomials based on constrained learning neural networks', Physics Letters, Section A: General, Atomic and Solid State Physics, vol. 309, no. 5-6, pp. 443-451. https://doi.org/10.1016/S0375-9601(03)00216-0

Huang, D-S., Ip, H. H. S., Chi, Z., & Wong, H. S. (2003). Dilation method for finding close roots of polynomials based on constrained learning neural networks. Physics Letters, Section A: General, Atomic and Solid State Physics, 309(5-6), 443-451. https://doi.org/10.1016/S0375-9601(03)00216-0

Huang D-S, Ip HHS, Chi Z, Wong HS. Dilation method for finding close roots of polynomials based on constrained learning neural networks. Physics Letters, Section A: General, Atomic and Solid State Physics. 2003 Mar 31;309(5-6):443-451. doi: 10.1016/S0375-9601(03)00216-0

Huang, De-Shuang ; Ip, Horace H.S. ; Chi, Zheru et al. / Dilation method for finding close roots of polynomials based on constrained learning neural networks. In: Physics Letters, Section A: General, Atomic and Solid State Physics. 2003 ; Vol. 309, No. 5-6. pp. 443-451.