Some extensions of the lanczos-ortiz theory of canonical polynomials in the tau method

Detalhes bibliográficos
Autor(a) principal: Bunchaft, M. E. Froes
Data de Publicação: 1997
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UFBA
Texto Completo: http://www.repositorio.ufba.br/ri/handle/ri/12758
Resumo: p. 609-621
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spelling Bunchaft, M. E. FroesBunchaft, M. E. Froes2013-08-27T17:33:01Z2013-08-27T17:33:01Z19970025-5718http://www.repositorio.ufba.br/ri/handle/ri/12758v. 66, n. 218p. 609-621Lanczos and Ortiz placed the canonical polynomials (c.p.'s) in a central position in the Tau Method. In addition, Ortiz devised a recursive process for determining c.p.'s consisting of a generating formula and a complementary algorithm coupled to the formula. In this paper a) We extend the theory so as to include in the formalism also the ordinary linear di erential operators with polynomial coe cients D with negative height h = max n2Nfmn −ng < 0; where mn denotes the degree of Dxn. b) We establish a basic classi cation of the c.p.'s Qm(x) and their orders m 2 M, as primary or derived, depending, respectively, on whether 9n 2 N: mn = m or such n does not exist; and we state a classi cation of the indices n 2 N, as generic (mn = n+h), singular (mn < n+h), and inde nite (Dxn 0). Then a formula which gives the set of primary orders is proved. c) In the rather frequent case in which all c.p.'s are primary, we establish, for di erential operators D with any height h, a recurrency formula which generates bases of the polynomial space and their multiple c.p.'s arising from distinct xn, n 2 N, so that no complementary algorithmic construction is needed; the (primary) c.p.'s so produced are classi ed as generic or singular, depending on the index n. d) We establish the general properties of the multiplicity relations of the primary c.p.'s and of their associated indices. It becomes clear that Ortiz's formula generates, for h 0, the generic c.p.'s in terms of the singular and derived c.p.'s, while singular and derived c.p.'s and the multiples of distinct indices are constructed by the algorithm.Submitted by Santiago Fabio (fabio.ssantiago@hotmail.com) on 2013-08-27T17:33:01Z No. of bitstreams: 1 11111111111.pdf: 347378 bytes, checksum: 5798b30170159d882b0ff5fa6729c449 (MD5)Made available in DSpace on 2013-08-27T17:33:01Z (GMT). No. of bitstreams: 1 11111111111.pdf: 347378 bytes, checksum: 5798b30170159d882b0ff5fa6729c449 (MD5) Previous issue date: 1997SalvadorMathematics of Computationhttp://www.ams.org/journals/mcom/1997-66-218/S0025-5718-97-00816-8/S0025-5718-97-00816-8.pdfreponame:Repositório Institucional da UFBAinstname:Universidade Federal da Bahia (UFBA)instacron:UFBASome extensions of the lanczos-ortiz theory of canonical polynomials in the tau methodMathematics of Computationinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleenginfo:eu-repo/semantics/openAccessORIGINAL11111111111.pdf11111111111.pdfapplication/pdf347378https://repositorio.ufba.br/bitstream/ri/12758/1/11111111111.pdf5798b30170159d882b0ff5fa6729c449MD51LICENSElicense.txtlicense.txttext/plain1762https://repositorio.ufba.br/bitstream/ri/12758/2/license.txt1b89a9a0548218172d7c829f87a0eab9MD52ri/127582022-07-05 14:02:49.77oai:repositorio.ufba.br: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Repositório InstitucionalPUBhttp://192.188.11.11:8080/oai/requestopendoar:19322022-07-05T17:02:49Repositório Institucional da UFBA - Universidade Federal da Bahia (UFBA)false
dc.title.pt_BR.fl_str_mv Some extensions of the lanczos-ortiz theory of canonical polynomials in the tau method
dc.title.alternative.pt_BR.fl_str_mv Mathematics of Computation
title Some extensions of the lanczos-ortiz theory of canonical polynomials in the tau method
spellingShingle Some extensions of the lanczos-ortiz theory of canonical polynomials in the tau method
Bunchaft, M. E. Froes
title_short Some extensions of the lanczos-ortiz theory of canonical polynomials in the tau method
title_full Some extensions of the lanczos-ortiz theory of canonical polynomials in the tau method
title_fullStr Some extensions of the lanczos-ortiz theory of canonical polynomials in the tau method
title_full_unstemmed Some extensions of the lanczos-ortiz theory of canonical polynomials in the tau method
title_sort Some extensions of the lanczos-ortiz theory of canonical polynomials in the tau method
author Bunchaft, M. E. Froes
author_facet Bunchaft, M. E. Froes
author_role author
dc.contributor.author.fl_str_mv Bunchaft, M. E. Froes
Bunchaft, M. E. Froes
description p. 609-621
publishDate 1997
dc.date.issued.fl_str_mv 1997
dc.date.accessioned.fl_str_mv 2013-08-27T17:33:01Z
dc.date.available.fl_str_mv 2013-08-27T17:33:01Z
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://www.repositorio.ufba.br/ri/handle/ri/12758
dc.identifier.issn.none.fl_str_mv 0025-5718
dc.identifier.number.pt_BR.fl_str_mv v. 66, n. 218
identifier_str_mv 0025-5718
v. 66, n. 218
url http://www.repositorio.ufba.br/ri/handle/ri/12758
dc.language.iso.fl_str_mv eng
language eng
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv Mathematics of Computation
publisher.none.fl_str_mv Mathematics of Computation
dc.source.pt_BR.fl_str_mv http://www.ams.org/journals/mcom/1997-66-218/S0025-5718-97-00816-8/S0025-5718-97-00816-8.pdf
dc.source.none.fl_str_mv reponame:Repositório Institucional da UFBA
instname:Universidade Federal da Bahia (UFBA)
instacron:UFBA
instname_str Universidade Federal da Bahia (UFBA)
instacron_str UFBA
institution UFBA
reponame_str Repositório Institucional da UFBA
collection Repositório Institucional da UFBA
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