Computing the zeros of quaternion polynomials

Detalhes bibliográficos
Autor(a) principal: Serôdio, R.
Data de Publicação: 2001
Outros Autores: Pereira, E., Vitória, J.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10316/4646
https://doi.org/10.1016/S0898-1221(01)00235-8
Resumo: A method is developed to compute the zeros of a quaternion polynomial with all terms of the form qkXk. This method is based essentially in Niven's algorithm [1], which consists of dividing the polynomial by a characteristic polynomial associated to a zero. The information about the trace and the norm of the zero is obtained by an original idea which requires the companion matrix associated to the polynomial. The companion matrix is represented by a matrix with complex entries. Three numerical examples using Mathematica 2.2 version are given.
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spelling Computing the zeros of quaternion polynomialsRight (and left) quaternionic eigenvaluesQuaternionic polynomialsCompanion quaternionic matrixA method is developed to compute the zeros of a quaternion polynomial with all terms of the form qkXk. This method is based essentially in Niven's algorithm [1], which consists of dividing the polynomial by a characteristic polynomial associated to a zero. The information about the trace and the norm of the zero is obtained by an original idea which requires the companion matrix associated to the polynomial. The companion matrix is represented by a matrix with complex entries. Three numerical examples using Mathematica 2.2 version are given.http://www.sciencedirect.com/science/article/B6TYJ-444G6J6-N/1/2ab1f648c1929ffc5374c2a8b11c2a772001info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleaplication/PDFhttp://hdl.handle.net/10316/4646http://hdl.handle.net/10316/4646https://doi.org/10.1016/S0898-1221(01)00235-8engComputers & Mathematics with Applications. 42:8-9 (2001) 1229-1237Serôdio, R.Pereira, E.Vitória, J.info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2020-11-06T16:59:53Zoai:estudogeral.uc.pt:10316/4646Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T21:00:42.344625Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv Computing the zeros of quaternion polynomials
title Computing the zeros of quaternion polynomials
spellingShingle Computing the zeros of quaternion polynomials
Serôdio, R.
Right (and left) quaternionic eigenvalues
Quaternionic polynomials
Companion quaternionic matrix
title_short Computing the zeros of quaternion polynomials
title_full Computing the zeros of quaternion polynomials
title_fullStr Computing the zeros of quaternion polynomials
title_full_unstemmed Computing the zeros of quaternion polynomials
title_sort Computing the zeros of quaternion polynomials
author Serôdio, R.
author_facet Serôdio, R.
Pereira, E.
Vitória, J.
author_role author
author2 Pereira, E.
Vitória, J.
author2_role author
author
dc.contributor.author.fl_str_mv Serôdio, R.
Pereira, E.
Vitória, J.
dc.subject.por.fl_str_mv Right (and left) quaternionic eigenvalues
Quaternionic polynomials
Companion quaternionic matrix
topic Right (and left) quaternionic eigenvalues
Quaternionic polynomials
Companion quaternionic matrix
description A method is developed to compute the zeros of a quaternion polynomial with all terms of the form qkXk. This method is based essentially in Niven's algorithm [1], which consists of dividing the polynomial by a characteristic polynomial associated to a zero. The information about the trace and the norm of the zero is obtained by an original idea which requires the companion matrix associated to the polynomial. The companion matrix is represented by a matrix with complex entries. Three numerical examples using Mathematica 2.2 version are given.
publishDate 2001
dc.date.none.fl_str_mv 2001
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10316/4646
http://hdl.handle.net/10316/4646
https://doi.org/10.1016/S0898-1221(01)00235-8
url http://hdl.handle.net/10316/4646
https://doi.org/10.1016/S0898-1221(01)00235-8
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Computers & Mathematics with Applications. 42:8-9 (2001) 1229-1237
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv aplication/PDF
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
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