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Article: Relationship between the zeros of two polynomials

TitleRelationship between the zeros of two polynomials
Authors
KeywordsD-companion matrices
Polynomials
Schoenberg conjecture
Sendov conjecture
Weinstein-Aronszajn Formula
Zeros
Issue Date2010
PublisherElsevier Inc. The Journal's web site is located at http://www.elsevier.com/locate/laa
Citation
Linear Algebra And Its Applications, 2010, v. 432 n. 1, p. 107-115 How to Cite?
AbstractIn this paper, we shall follow a companion matrix approach to study the relationship between zeros of a wide range of pairs of complex polynomials, for example, a polynomial and its polar derivative or Sz.-Nagy's generalized derivative. We shall introduce some new companion matrices and obtain a generalization of the Weinstein-Aronszajn Formula which will then be used to prove some inequalities similar to Sendov conjecture and Schoenberg conjecture and to study the distribution of equilibrium points of logarithmic potentials for finitely many discrete charges. Our method can also be used to produce, in an easy and systematic way, a lot of identities relating the sums of powers of zeros of a polynomial to that of the other polynomial. © 2009 Elsevier Inc.
Persistent Identifierhttp://hdl.handle.net/10722/144763
ISSN
2015 Impact Factor: 0.965
2015 SCImago Journal Rankings: 0.837
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorCheung, WSen_HK
dc.contributor.authorNg, TWen_HK
dc.date.accessioned2012-02-03T09:22:40Z-
dc.date.available2012-02-03T09:22:40Z-
dc.date.issued2010en_HK
dc.identifier.citationLinear Algebra And Its Applications, 2010, v. 432 n. 1, p. 107-115en_HK
dc.identifier.issn0024-3795en_HK
dc.identifier.urihttp://hdl.handle.net/10722/144763-
dc.description.abstractIn this paper, we shall follow a companion matrix approach to study the relationship between zeros of a wide range of pairs of complex polynomials, for example, a polynomial and its polar derivative or Sz.-Nagy's generalized derivative. We shall introduce some new companion matrices and obtain a generalization of the Weinstein-Aronszajn Formula which will then be used to prove some inequalities similar to Sendov conjecture and Schoenberg conjecture and to study the distribution of equilibrium points of logarithmic potentials for finitely many discrete charges. Our method can also be used to produce, in an easy and systematic way, a lot of identities relating the sums of powers of zeros of a polynomial to that of the other polynomial. © 2009 Elsevier Inc.en_HK
dc.languageeng-
dc.publisherElsevier Inc. The Journal's web site is located at http://www.elsevier.com/locate/laaen_HK
dc.relation.ispartofLinear Algebra and Its Applicationsen_HK
dc.rightsNOTICE: this is the author’s version of a work that was accepted for publication in Linear Algebra and Its Applications. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Linear Algebra and Its Applications, [VOL 432, ISSUE 1, 2010] DOI 10.1016/j.laa.2009.07.028-
dc.subjectD-companion matricesen_HK
dc.subjectPolynomialsen_HK
dc.subjectSchoenberg conjectureen_HK
dc.subjectSendov conjectureen_HK
dc.subjectWeinstein-Aronszajn Formulaen_HK
dc.subjectZerosen_HK
dc.titleRelationship between the zeros of two polynomialsen_HK
dc.typeArticleen_HK
dc.identifier.emailNg, TW:ntw@maths.hku.hken_HK
dc.identifier.authorityNg, TW=rp00768en_HK
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1016/j.laa.2009.07.028en_HK
dc.identifier.scopuseid_2-s2.0-70449523087en_HK
dc.identifier.hkuros170452-
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-70449523087&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume432en_HK
dc.identifier.issue1en_HK
dc.identifier.spage107en_HK
dc.identifier.epage115en_HK
dc.identifier.eissn1873-1856-
dc.identifier.isiWOS:000272954400010-
dc.publisher.placeUnited Statesen_HK
dc.identifier.scopusauthoridCheung, WS=7202743043en_HK
dc.identifier.scopusauthoridNg, TW=7402229732en_HK
dc.identifier.citeulike5718896-

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