Explicit inverse of a tridiagonal k-Toeplitz matrix
Autor(a) principal: | |
---|---|
Data de Publicação: | 2005 |
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/10316/7740 https://doi.org/10.1007/s00211-005-0596-3 |
Resumo: | Summary We obtain explicit formulas for the entries of the inverse of a nonsingular and irreducible tridiagonal k-Toeplitz matrix A. The proof is based on results from the theory of orthogonal polynomials and it is shown that the entries of the inverse of such a matrix are given in terms of Chebyshev polynomials of the second kind. We also compute the characteristic polynomial of A which enables us to state some conditions for the existence of A-1. Our results also extend known results for the case when the residue mod k of the order of A is equal to 0 or k-1 (Numer. Math., 10 (1967), pp. 153–161.). |
id |
RCAP_16ef8ba6a482d8aa817a6ecea6921183 |
---|---|
oai_identifier_str |
oai:estudogeral.uc.pt:10316/7740 |
network_acronym_str |
RCAP |
network_name_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository_id_str |
7160 |
spelling |
Explicit inverse of a tridiagonal k-Toeplitz matrixSummary We obtain explicit formulas for the entries of the inverse of a nonsingular and irreducible tridiagonal k-Toeplitz matrix A. The proof is based on results from the theory of orthogonal polynomials and it is shown that the entries of the inverse of such a matrix are given in terms of Chebyshev polynomials of the second kind. We also compute the characteristic polynomial of A which enables us to state some conditions for the existence of A-1. Our results also extend known results for the case when the residue mod k of the order of A is equal to 0 or k-1 (Numer. Math., 10 (1967), pp. 153–161.).2005info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://hdl.handle.net/10316/7740http://hdl.handle.net/10316/7740https://doi.org/10.1007/s00211-005-0596-3engNumerische Mathematik. 100:3 (2005) 457-482Fonseca, C. M. daPetronilho, 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:RCAAP2020-05-25T13:06:04Zoai:estudogeral.uc.pt:10316/7740Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T21:00:39.919744Repositório 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 |
Explicit inverse of a tridiagonal k-Toeplitz matrix |
title |
Explicit inverse of a tridiagonal k-Toeplitz matrix |
spellingShingle |
Explicit inverse of a tridiagonal k-Toeplitz matrix Fonseca, C. M. da |
title_short |
Explicit inverse of a tridiagonal k-Toeplitz matrix |
title_full |
Explicit inverse of a tridiagonal k-Toeplitz matrix |
title_fullStr |
Explicit inverse of a tridiagonal k-Toeplitz matrix |
title_full_unstemmed |
Explicit inverse of a tridiagonal k-Toeplitz matrix |
title_sort |
Explicit inverse of a tridiagonal k-Toeplitz matrix |
author |
Fonseca, C. M. da |
author_facet |
Fonseca, C. M. da Petronilho, J. |
author_role |
author |
author2 |
Petronilho, J. |
author2_role |
author |
dc.contributor.author.fl_str_mv |
Fonseca, C. M. da Petronilho, J. |
description |
Summary We obtain explicit formulas for the entries of the inverse of a nonsingular and irreducible tridiagonal k-Toeplitz matrix A. The proof is based on results from the theory of orthogonal polynomials and it is shown that the entries of the inverse of such a matrix are given in terms of Chebyshev polynomials of the second kind. We also compute the characteristic polynomial of A which enables us to state some conditions for the existence of A-1. Our results also extend known results for the case when the residue mod k of the order of A is equal to 0 or k-1 (Numer. Math., 10 (1967), pp. 153–161.). |
publishDate |
2005 |
dc.date.none.fl_str_mv |
2005 |
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/10316/7740 http://hdl.handle.net/10316/7740 https://doi.org/10.1007/s00211-005-0596-3 |
url |
http://hdl.handle.net/10316/7740 https://doi.org/10.1007/s00211-005-0596-3 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Numerische Mathematik. 100:3 (2005) 457-482 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
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 |
instname_str |
Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
instacron_str |
RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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 |
repository.mail.fl_str_mv |
|
_version_ |
1799133897093545984 |