Quadrature rules from a R I I type recurrence relation and associated quadrature rules on the unit circle

Detalhes bibliográficos
Autor(a) principal: Bracciali, Cleonice F. [UNESP]
Data de Publicação: 2019
Outros Autores: Pereira, Junior A. [UNESP], Ranga, A. Sri [UNESP]
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UNESP
Texto Completo: http://dx.doi.org/10.1007/s11075-019-00714-w
http://hdl.handle.net/11449/189090
Resumo: We consider the theoretical and numerical aspects of the quadrature rules associated with a sequence of polynomials generated by a special R II recurrence relation. We also look into some methods for generating the nodes (which lie on the real line) and the positive weights of these quadrature rules. With a simple transformation, these quadrature rules on the real line also lead to certain positive quadrature rules of highest algebraic degree of precision on the unit circle. This way, we also introduce new approaches to evaluate the nodes and weights of these specific quadrature rules on the unit circle.
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spelling Quadrature rules from a R I I type recurrence relation and associated quadrature rules on the unit circleOrthogonal polynomials on the unit circleQuadrature rulesR II type recurrence relationWe consider the theoretical and numerical aspects of the quadrature rules associated with a sequence of polynomials generated by a special R II recurrence relation. We also look into some methods for generating the nodes (which lie on the real line) and the positive weights of these quadrature rules. With a simple transformation, these quadrature rules on the real line also lead to certain positive quadrature rules of highest algebraic degree of precision on the unit circle. This way, we also introduce new approaches to evaluate the nodes and weights of these specific quadrature rules on the unit circle.IBILCE Departamento de Matemática Aplicada UNESP – Universidade Estadual PaulistaIBILCE Departamento de Matemática Aplicada UNESP – Universidade Estadual PaulistaUniversidade Estadual Paulista (Unesp)Bracciali, Cleonice F. [UNESP]Pereira, Junior A. [UNESP]Ranga, A. Sri [UNESP]2019-10-06T16:29:28Z2019-10-06T16:29:28Z2019-01-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://dx.doi.org/10.1007/s11075-019-00714-wNumerical Algorithms.1572-92651017-1398http://hdl.handle.net/11449/18909010.1007/s11075-019-00714-w2-s2.0-8506538830783003224526224670000-0002-6823-4204Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengNumerical Algorithmsinfo:eu-repo/semantics/openAccess2022-02-09T11:19:33Zoai:repositorio.unesp.br:11449/189090Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462022-02-09T11:19:33Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv Quadrature rules from a R I I type recurrence relation and associated quadrature rules on the unit circle
title Quadrature rules from a R I I type recurrence relation and associated quadrature rules on the unit circle
spellingShingle Quadrature rules from a R I I type recurrence relation and associated quadrature rules on the unit circle
Bracciali, Cleonice F. [UNESP]
Orthogonal polynomials on the unit circle
Quadrature rules
R II type recurrence relation
title_short Quadrature rules from a R I I type recurrence relation and associated quadrature rules on the unit circle
title_full Quadrature rules from a R I I type recurrence relation and associated quadrature rules on the unit circle
title_fullStr Quadrature rules from a R I I type recurrence relation and associated quadrature rules on the unit circle
title_full_unstemmed Quadrature rules from a R I I type recurrence relation and associated quadrature rules on the unit circle
title_sort Quadrature rules from a R I I type recurrence relation and associated quadrature rules on the unit circle
author Bracciali, Cleonice F. [UNESP]
author_facet Bracciali, Cleonice F. [UNESP]
Pereira, Junior A. [UNESP]
Ranga, A. Sri [UNESP]
author_role author
author2 Pereira, Junior A. [UNESP]
Ranga, A. Sri [UNESP]
author2_role author
author
dc.contributor.none.fl_str_mv Universidade Estadual Paulista (Unesp)
dc.contributor.author.fl_str_mv Bracciali, Cleonice F. [UNESP]
Pereira, Junior A. [UNESP]
Ranga, A. Sri [UNESP]
dc.subject.por.fl_str_mv Orthogonal polynomials on the unit circle
Quadrature rules
R II type recurrence relation
topic Orthogonal polynomials on the unit circle
Quadrature rules
R II type recurrence relation
description We consider the theoretical and numerical aspects of the quadrature rules associated with a sequence of polynomials generated by a special R II recurrence relation. We also look into some methods for generating the nodes (which lie on the real line) and the positive weights of these quadrature rules. With a simple transformation, these quadrature rules on the real line also lead to certain positive quadrature rules of highest algebraic degree of precision on the unit circle. This way, we also introduce new approaches to evaluate the nodes and weights of these specific quadrature rules on the unit circle.
publishDate 2019
dc.date.none.fl_str_mv 2019-10-06T16:29:28Z
2019-10-06T16:29:28Z
2019-01-01
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://dx.doi.org/10.1007/s11075-019-00714-w
Numerical Algorithms.
1572-9265
1017-1398
http://hdl.handle.net/11449/189090
10.1007/s11075-019-00714-w
2-s2.0-85065388307
8300322452622467
0000-0002-6823-4204
url http://dx.doi.org/10.1007/s11075-019-00714-w
http://hdl.handle.net/11449/189090
identifier_str_mv Numerical Algorithms.
1572-9265
1017-1398
10.1007/s11075-019-00714-w
2-s2.0-85065388307
8300322452622467
0000-0002-6823-4204
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Numerical Algorithms
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.source.none.fl_str_mv Scopus
reponame:Repositório Institucional da UNESP
instname:Universidade Estadual Paulista (UNESP)
instacron:UNESP
instname_str Universidade Estadual Paulista (UNESP)
instacron_str UNESP
institution UNESP
reponame_str Repositório Institucional da UNESP
collection Repositório Institucional da UNESP
repository.name.fl_str_mv Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)
repository.mail.fl_str_mv
_version_ 1803047204972134400

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