Bounds for sine and cosine via eigenvalue estimation

Detalhes bibliográficos
Autor(a) principal: Haukkanen, Pentti
Data de Publicação: 2014
Outros Autores: Mattila, Mika, Merikoski, Jorma K., Kovacec, Alexander
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10316/109685
https://doi.org/10.2478/spma-2014-0003
Resumo: De ne n × n tridiagonal matrices T and S as follows: All entries of the main diagonal of T are zero and those of the rst super- and subdiagonal are one. The entries of the main diagonal of S are two except the (n, n) entry one, and those of the rst super- and subdiagonal are minus one. Then, denoting by (·) the largest eigenvalue, (T) = 2 cos n + 1 , (S−1) = 1 4 cos2 n 2n+1 . Using certain lower bounds for the largest eigenvalue, we provide lower bounds for these expressions and, further, lower bounds for sin x and cos x on certain intervals. Also upper bounds can be obtained in this way.
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spelling Bounds for sine and cosine via eigenvalue estimationeigenvalue boundstrigonometric inequalitiesDe ne n × n tridiagonal matrices T and S as follows: All entries of the main diagonal of T are zero and those of the rst super- and subdiagonal are one. The entries of the main diagonal of S are two except the (n, n) entry one, and those of the rst super- and subdiagonal are minus one. Then, denoting by (·) the largest eigenvalue, (T) = 2 cos n + 1 , (S−1) = 1 4 cos2 n 2n+1 . Using certain lower bounds for the largest eigenvalue, we provide lower bounds for these expressions and, further, lower bounds for sin x and cos x on certain intervals. Also upper bounds can be obtained in this way.Walter de Gruyter2014info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://hdl.handle.net/10316/109685http://hdl.handle.net/10316/109685https://doi.org/10.2478/spma-2014-0003eng2300-7451Haukkanen, PenttiMattila, MikaMerikoski, Jorma K.Kovacec, Alexanderinfo: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:RCAAP2023-10-20T11:55:21Zoai:estudogeral.uc.pt:10316/109685Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T21:25:50.491932Repositório 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 Bounds for sine and cosine via eigenvalue estimation
title Bounds for sine and cosine via eigenvalue estimation
spellingShingle Bounds for sine and cosine via eigenvalue estimation
Haukkanen, Pentti
eigenvalue bounds
trigonometric inequalities
title_short Bounds for sine and cosine via eigenvalue estimation
title_full Bounds for sine and cosine via eigenvalue estimation
title_fullStr Bounds for sine and cosine via eigenvalue estimation
title_full_unstemmed Bounds for sine and cosine via eigenvalue estimation
title_sort Bounds for sine and cosine via eigenvalue estimation
author Haukkanen, Pentti
author_facet Haukkanen, Pentti
Mattila, Mika
Merikoski, Jorma K.
Kovacec, Alexander
author_role author
author2 Mattila, Mika
Merikoski, Jorma K.
Kovacec, Alexander
author2_role author
author
author
dc.contributor.author.fl_str_mv Haukkanen, Pentti
Mattila, Mika
Merikoski, Jorma K.
Kovacec, Alexander
dc.subject.por.fl_str_mv eigenvalue bounds
trigonometric inequalities
topic eigenvalue bounds
trigonometric inequalities
description De ne n × n tridiagonal matrices T and S as follows: All entries of the main diagonal of T are zero and those of the rst super- and subdiagonal are one. The entries of the main diagonal of S are two except the (n, n) entry one, and those of the rst super- and subdiagonal are minus one. Then, denoting by (·) the largest eigenvalue, (T) = 2 cos n + 1 , (S−1) = 1 4 cos2 n 2n+1 . Using certain lower bounds for the largest eigenvalue, we provide lower bounds for these expressions and, further, lower bounds for sin x and cos x on certain intervals. Also upper bounds can be obtained in this way.
publishDate 2014
dc.date.none.fl_str_mv 2014
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/10316/109685
http://hdl.handle.net/10316/109685
https://doi.org/10.2478/spma-2014-0003
url http://hdl.handle.net/10316/109685
https://doi.org/10.2478/spma-2014-0003
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 2300-7451
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv Walter de Gruyter
publisher.none.fl_str_mv Walter de Gruyter
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
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