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Ehrlich-type methods with king’s correction for the simultaneous approximation of polynomial complex zeros

2019Journal article Open access
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dc.contributor.authorNeves Machado, Roselaine
dc.contributor.authorLopes, Luiz Guerreiro
dc.date.accessioned2021-10-25T13:41:12Z
dc.date.available2021-10-25T13:41:12Z
dc.date.issued2019
dc.description.abstractThere are many simultaneous iterative methods for approximating complex polynomial zeros, from more traditional numerical algorithms, such as the well-known third order Ehrlich–Aberth method, to the more recent ones. In this paper, we present a new family of combined iterative methods for the simultaneous determination of simple complex zeros of a polynomial, which uses the Ehrlich iteration and a correction based on King’s family of iterative methods for nonlinear equations. The use of King’s correction allows increasing the convergence order of the basic method from three to six. Some numerical examples are given to illustrate the convergence behaviour and effectiveness of the proposed sixth order Ehrlich-like family of combined iterative methods for the simultaneous approximation of simple complex polynomial zeros. the advantage of being inherently parallel and avoid the pro cess of deflation, although these iterative methods usually need good initial approximations for all the zeros in order to con verge. In this work, a new family of numerical methods for the si multaneous approximation of simple complex polynomial ze ros is presented. The proposed simultaneous methods are con structed on the basis of the well-known third order Ehrlich– Aberth iteration [1, 6], combined with an iterative correction from the optimal fourth order two-step King’s method for solv ing nonlinear equations [10]pt_PT
dc.description.versioninfo:eu-repo/semantics/publishedVersionpt_PT
dc.identifier.citationMachado, R. N., & Lopes, L. G. (2019). Ehrlich-type methods with King’s correction for the simultaneous approximation of polynomial complex zeros. Mathematics and Statistics, 7(4), 129-134. DOI: 10.13189/ms.2019.070406pt_PT
dc.identifier.doi10.13189/ms.2019.070406pt_PT
dc.identifier.urihttp://hdl.handle.net/10400.13/3761
dc.language.isoengpt_PT
dc.peerreviewedyespt_PT
dc.publisherHorizon Research Publishing (HRPUB)pt_PT
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/pt_PT
dc.subjectPolynomial zerospt_PT
dc.subjectSimultaneous iterative methodspt_PT
dc.subjectCombined methodspt_PT
dc.subjectEhrlich methodpt_PT
dc.subject.pt_PT
dc.subjectFaculdade de Ciências Exatas e da Engenhariapt_PT
dc.titleEhrlich-type methods with king’s correction for the simultaneous approximation of polynomial complex zerospt_PT
dc.typejournal article
dspace.entity.typePublication
oaire.citation.endPage134pt_PT
oaire.citation.issue4pt_PT
oaire.citation.startPage129pt_PT
oaire.citation.titleMathematics and Statisticspt_PT
oaire.citation.volume7pt_PT
person.familyNameGuerreiro Lopes
person.givenNameLuiz Carlos
person.identifierB-4961-2016
person.identifier.ciencia-id4A18-1DCB-4862
person.identifier.orcid0000-0002-6145-8520
person.identifier.scopus-author-id57205501523
rcaap.rightsopenAccesspt_PT
rcaap.typearticlept_PT
relation.isAuthorOfPublicationce1b7737-282b-479c-b3a9-b7fcdae90250
relation.isAuthorOfPublication.latestForDiscoveryce1b7737-282b-479c-b3a9-b7fcdae90250

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