Computing the zeros of quaternion polynomials
Main Author: | |
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Publication Date: | 2001 |
Other Authors: | , |
Format: | Article |
Language: | eng |
Source: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Download full: | http://hdl.handle.net/10316/4646 https://doi.org/10.1016/S0898-1221(01)00235-8 |
Summary: | 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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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 |
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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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