Evaluation schemes in the ring of quaternionic polynomials

Detalhes bibliográficos
Autor(a) principal: Falcão, M. I.
Data de Publicação: 2018
Outros Autores: Miranda, Fernando, Severino, Ricardo, Soares, M. 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/1822/54576
Resumo: In this paper we focus on computational aspects associated with polynomial problems in the ring of one-sided quaternionic polynomials. The complexity and error bounds of quaternion arithmetic are considered and several evaluation schemes are analyzed from their complexity point of view. The numerical stability of generalized Horner’s and Goertzel’s algorithms to evaluate polynomials with quaternion floating-point coefficients is addressed. Numerical tests illustrate the behavior of the algorithms from the point of view of performance and accuracy.
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spelling Evaluation schemes in the ring of quaternionic polynomialsError analysisPolynomial evaluationQuaternionsScience & TechnologyIn this paper we focus on computational aspects associated with polynomial problems in the ring of one-sided quaternionic polynomials. The complexity and error bounds of quaternion arithmetic are considered and several evaluation schemes are analyzed from their complexity point of view. The numerical stability of generalized Horner’s and Goertzel’s algorithms to evaluate polynomials with quaternion floating-point coefficients is addressed. Numerical tests illustrate the behavior of the algorithms from the point of view of performance and accuracy.Research at CMAT was financed by Portuguese Funds through FCT - Fundação para a Ciência e a Tecnologia, within the Project UID/MAT/00013/2013. Research at NIPE was carried out within the funding with COMPETE reference number POCI-01-0145-FEDER-006683 (UID/ECO/03182/2013), with the FCT/MEC’s (Fundação para a Ciência 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.info:eu-repo/semantics/publishedVersionSpringerUniversidade do MinhoFalcão, M. I.Miranda, FernandoSeverino, RicardoSoares, M. J.20182018-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/1822/54576eng0006-383510.1007/s10543-017-0667-8info: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:RCAAP2023-07-21T12:51:45Zoai:repositorium.sdum.uminho.pt:1822/54576Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T19:50:43.843928Repositório 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 Evaluation schemes in the ring of quaternionic polynomials
title Evaluation schemes in the ring of quaternionic polynomials
spellingShingle Evaluation schemes in the ring of quaternionic polynomials
Falcão, M. I.
Error analysis
Polynomial evaluation
Quaternions
Science & Technology
title_short Evaluation schemes in the ring of quaternionic polynomials
title_full Evaluation schemes in the ring of quaternionic polynomials
title_fullStr Evaluation schemes in the ring of quaternionic polynomials
title_full_unstemmed Evaluation schemes in the ring of quaternionic polynomials
title_sort Evaluation schemes in the ring of quaternionic polynomials
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 Error analysis
Polynomial evaluation
Quaternions
Science & Technology
topic Error analysis
Polynomial evaluation
Quaternions
Science & Technology
description In this paper we focus on computational aspects associated with polynomial problems in the ring of one-sided quaternionic polynomials. The complexity and error bounds of quaternion arithmetic are considered and several evaluation schemes are analyzed from their complexity point of view. The numerical stability of generalized Horner’s and Goertzel’s algorithms to evaluate polynomials with quaternion floating-point coefficients is addressed. Numerical tests illustrate the behavior of the algorithms from the point of view of performance and accuracy.
publishDate 2018
dc.date.none.fl_str_mv 2018
2018-01-01T00:00:00Z
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/1822/54576
url http://hdl.handle.net/1822/54576
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 0006-3835
10.1007/s10543-017-0667-8
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 Springer
publisher.none.fl_str_mv Springer
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
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instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
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collection Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository.name.fl_str_mv Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
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