The number of zeros of unilateral polynomials over coquaternions revisited
Autor(a) principal: | |
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Data de Publicação: | 2019 |
Outros Autores: | , , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/1822/65607 |
Resumo: | The literature on quaternionic polynomials and, in particular, on methods for finding and classifying their zero sets, is fast developing and reveals a growing interest in this subject. In contrast, polynomials defined over the algebra of coquaternions have received very little attention from researchers. One of the few exceptions is the very recent paper by Janovska and Opfer [Electron Trans Numer Anal. 2017;46:55-70], where, among other results, we can find a first attempt to prove that a unilateral coquaternionic polynomial of degree n has, at most, zeros. In this paper we present a full proof of this result, using a totally different and, from our point of view, much simpler approach. Also, we give a complete characterization of the zero sets of such polynomials and present a new result giving conditions which guarantee the existence of a special type of zeros. An algorithm to compute and classify all the zeros of a coquaternionic polynomial is proposed and several numerical examples are carefully constructed. |
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The number of zeros of unilateral polynomials over coquaternions revisitedCoquaternionscoquaternionic polynomialscompanion polynomialadmissible classes12E0515A6665H04Ciências Naturais::MatemáticasScience & TechnologyThe literature on quaternionic polynomials and, in particular, on methods for finding and classifying their zero sets, is fast developing and reveals a growing interest in this subject. In contrast, polynomials defined over the algebra of coquaternions have received very little attention from researchers. One of the few exceptions is the very recent paper by Janovska and Opfer [Electron Trans Numer Anal. 2017;46:55-70], where, among other results, we can find a first attempt to prove that a unilateral coquaternionic polynomial of degree n has, at most, zeros. In this paper we present a full proof of this result, using a totally different and, from our point of view, much simpler approach. Also, we give a complete characterization of the zero sets of such polynomials and present a new result giving conditions which guarantee the existence of a special type of zeros. An algorithm to compute and classify all the zeros of a coquaternionic polynomial is proposed and several numerical examples are carefully constructed.Research at CMAT was financed by Portuguese Funds through FCT -Fundacao para a Ciencia e a Tecnologia, within the [project number UID/MAT/00013/2013]. Research at NIPE was carried out within the funding with COMPETE reference number POCI-01-0145-FEDER-006683 [project number UID/ECO/03182/2013], with the FCT/MEC's (Fundacao para a Ciencia e a Tecnologia, I.P.) financial support through national funding and by the ERDF through the Operational Programme on 'Competitiveness and Internationalization - COMPETE 2020' under the PT2020 Partnership Agreement.Taylor & Francis LtdUniversidade do MinhoFalcão, M. I.Miranda, FernandoSeverino, RicardoSoares, M. J.2019-06-032019-06-03T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/1822/65607eng0308-108710.1080/03081087.2018.1450828https://www.tandfonline.com/doi/full/10.1080/03081087.2018.1450828info: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:RCAAP2023-07-21T12:54:06Zoai:repositorium.sdum.uminho.pt:1822/65607Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T19:53:38.757119Repositório 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 |
The number of zeros of unilateral polynomials over coquaternions revisited |
title |
The number of zeros of unilateral polynomials over coquaternions revisited |
spellingShingle |
The number of zeros of unilateral polynomials over coquaternions revisited Falcão, M. I. Coquaternions coquaternionic polynomials companion polynomial admissible classes 12E05 15A66 65H04 Ciências Naturais::Matemáticas Science & Technology |
title_short |
The number of zeros of unilateral polynomials over coquaternions revisited |
title_full |
The number of zeros of unilateral polynomials over coquaternions revisited |
title_fullStr |
The number of zeros of unilateral polynomials over coquaternions revisited |
title_full_unstemmed |
The number of zeros of unilateral polynomials over coquaternions revisited |
title_sort |
The number of zeros of unilateral polynomials over coquaternions revisited |
author |
Falcão, M. I. |
author_facet |
Falcão, M. I. Miranda, Fernando Severino, Ricardo Soares, M. J. |
author_role |
author |
author2 |
Miranda, Fernando Severino, Ricardo Soares, M. J. |
author2_role |
author author author |
dc.contributor.none.fl_str_mv |
Universidade do Minho |
dc.contributor.author.fl_str_mv |
Falcão, M. I. Miranda, Fernando Severino, Ricardo Soares, M. J. |
dc.subject.por.fl_str_mv |
Coquaternions coquaternionic polynomials companion polynomial admissible classes 12E05 15A66 65H04 Ciências Naturais::Matemáticas Science & Technology |
topic |
Coquaternions coquaternionic polynomials companion polynomial admissible classes 12E05 15A66 65H04 Ciências Naturais::Matemáticas Science & Technology |
description |
The literature on quaternionic polynomials and, in particular, on methods for finding and classifying their zero sets, is fast developing and reveals a growing interest in this subject. In contrast, polynomials defined over the algebra of coquaternions have received very little attention from researchers. One of the few exceptions is the very recent paper by Janovska and Opfer [Electron Trans Numer Anal. 2017;46:55-70], where, among other results, we can find a first attempt to prove that a unilateral coquaternionic polynomial of degree n has, at most, zeros. In this paper we present a full proof of this result, using a totally different and, from our point of view, much simpler approach. Also, we give a complete characterization of the zero sets of such polynomials and present a new result giving conditions which guarantee the existence of a special type of zeros. An algorithm to compute and classify all the zeros of a coquaternionic polynomial is proposed and several numerical examples are carefully constructed. |
publishDate |
2019 |
dc.date.none.fl_str_mv |
2019-06-03 2019-06-03T00:00:00Z |
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/1822/65607 |
url |
http://hdl.handle.net/1822/65607 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
0308-1087 10.1080/03081087.2018.1450828 https://www.tandfonline.com/doi/full/10.1080/03081087.2018.1450828 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
Taylor & Francis Ltd |
publisher.none.fl_str_mv |
Taylor & Francis Ltd |
dc.source.none.fl_str_mv |
reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
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Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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RCAAP |
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RCAAP |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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