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Article: A companion matrix approach to the study of zeros and critical points of a polynomial

TitleA companion matrix approach to the study of zeros and critical points of a polynomial
Authors
KeywordsCritical Points
D-Companion Matrices
De Bruin And Sharma Conjecture
Gerschgorin's Disks
Majorization
Ovals Of Cassini
Polynomials
Schoenberg Conjecture
Zeros
Issue Date2006
PublisherAcademic Press. The Journal's web site is located at http://www.elsevier.com/locate/jmaa
Citation
Journal of Mathematical Analysis and Applications, 2006, v. 319 n. 2, p. 690-707 How to Cite?
AbstractIn this paper, we introduce a new type of companion matrices, namely, D-companion matrices. By using these D-companion matrices, we are able to apply matrix theory directly to study the geometrical relation between the zeros and critical points of a polynomial. In fact, this new approach will allow us to prove quite a number of new as well as known results on this topic. For example, we prove some results on the majorization of the critical points of a polynomial by its zeros. In particular, we give a different proof of a recent result of Gerhard Schmeisser on this topic. The same method allows us to prove a higher order Schoenberg-type conjecture proposed by M.G. de Bruin and A. Sharma. © 2005 Elsevier Inc. All rights reserved.
Persistent Identifierhttp://hdl.handle.net/10722/156163
ISSN
2015 Impact Factor: 1.014
2015 SCImago Journal Rankings: 1.161
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorCheung, WSen_US
dc.contributor.authorNg, TWen_US
dc.date.accessioned2012-08-08T08:40:40Z-
dc.date.available2012-08-08T08:40:40Z-
dc.date.issued2006en_US
dc.identifier.citationJournal of Mathematical Analysis and Applications, 2006, v. 319 n. 2, p. 690-707en_US
dc.identifier.issn0022-247Xen_US
dc.identifier.urihttp://hdl.handle.net/10722/156163-
dc.description.abstractIn this paper, we introduce a new type of companion matrices, namely, D-companion matrices. By using these D-companion matrices, we are able to apply matrix theory directly to study the geometrical relation between the zeros and critical points of a polynomial. In fact, this new approach will allow us to prove quite a number of new as well as known results on this topic. For example, we prove some results on the majorization of the critical points of a polynomial by its zeros. In particular, we give a different proof of a recent result of Gerhard Schmeisser on this topic. The same method allows us to prove a higher order Schoenberg-type conjecture proposed by M.G. de Bruin and A. Sharma. © 2005 Elsevier Inc. All rights reserved.en_US
dc.languageengen_US
dc.publisherAcademic Press. The Journal's web site is located at http://www.elsevier.com/locate/jmaaen_US
dc.relation.ispartofJournal of Mathematical Analysis and Applicationsen_US
dc.rightsNOTICE: this is the author’s version of a work that was accepted for publication in <Journal of Mathematical Analysis and 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 PUBLICATION, [2006, v. 319 n. 2] DOI# 10.1016/j.jmaa.2005.06.071-
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.subjectCritical Pointsen_US
dc.subjectD-Companion Matricesen_US
dc.subjectDe Bruin And Sharma Conjectureen_US
dc.subjectGerschgorin's Disksen_US
dc.subjectMajorizationen_US
dc.subjectOvals Of Cassinien_US
dc.subjectPolynomialsen_US
dc.subjectSchoenberg Conjectureen_US
dc.subjectZerosen_US
dc.titleA companion matrix approach to the study of zeros and critical points of a polynomialen_US
dc.typeArticleen_US
dc.identifier.emailNg, TW:ntw@maths.hku.hken_US
dc.identifier.authorityNg, TW=rp00768en_US
dc.description.naturepreprinten_US
dc.identifier.doi10.1016/j.jmaa.2005.06.071en_US
dc.identifier.scopuseid_2-s2.0-33645975793en_US
dc.identifier.hkuros116489-
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-33645975793&selection=ref&src=s&origin=recordpageen_US
dc.identifier.volume319en_US
dc.identifier.issue2en_US
dc.identifier.spage690en_US
dc.identifier.epage707en_US
dc.identifier.eissn1096-0813-
dc.identifier.isiWOS:000240390700022-
dc.publisher.placeUnited Statesen_US
dc.identifier.scopusauthoridCheung, WS=7202743043en_US
dc.identifier.scopusauthoridNg, TW=7402229732en_US

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