Quadrature rules from a R I I type recurrence relation and associated quadrature rules on the unit circle
Autor(a) principal: | |
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Data de Publicação: | 2019 |
Outros Autores: | , |
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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Repositório Institucional da UNESP |
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2946 |
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_ |
1803650136019042304 |