Computing the first eigenvalue of the p-Laplacian via the inverse power method.
Autor(a) principal: | |
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Data de Publicação: | 2009 |
Outros Autores: | , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UFOP |
Texto Completo: | http://www.repositorio.ufop.br/handle/123456789/1970 |
Resumo: | In this paper, we discuss a new method for computing the first Dirichlet eigenvalue of the p-Laplacian inspired by the inverse power method in finite dimensional linear algebra. The iterative technique is independent of the particular method used in solving the p-Laplacian equation and therefore can be made as efficient as the latter. The method is validated theoretically for any ball in Rn if p >1 and for any bounded domain in the particular case p = 2. For p >2 the method is validated numerically for the square. |
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Biezuner, Rodney JosuéErcole, GreyMartins, Eder Marinho2012-12-05T15:50:55Z2012-12-05T15:50:55Z2009BIEZUNER, R. J.; ERCOLE, G.; MARTINS, E. M. Computing the first eigenvalue of the p-Laplacian via the inverse power method. Journal of Functional Analysis, v. 257, n. 1, p. 243-270, 2009. Disponível em: <https://www.sciencedirect.com/science/article/pii/S0022123609000445>. Acesso em: 03 dez. 201200221236http://www.repositorio.ufop.br/handle/123456789/1970In this paper, we discuss a new method for computing the first Dirichlet eigenvalue of the p-Laplacian inspired by the inverse power method in finite dimensional linear algebra. The iterative technique is independent of the particular method used in solving the p-Laplacian equation and therefore can be made as efficient as the latter. The method is validated theoretically for any ball in Rn if p >1 and for any bounded domain in the particular case p = 2. For p >2 the method is validated numerically for the square.p-LaplacianFirst eigenvalueComparison principlePower methodComputing the first eigenvalue of the p-Laplacian via the inverse power method.info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleO periódico Journal of Functional Analysis concede permissão para depósito do artigo no Repositório Institucional da UFOP. Número da licença: 3305300201996.info:eu-repo/semantics/openAccessengreponame:Repositório Institucional da UFOPinstname:Universidade Federal de Ouro Preto (UFOP)instacron:UFOPLICENSElicense.txtlicense.txttext/plain; charset=utf-81748http://www.repositorio.ufop.br/bitstream/123456789/1970/2/license.txt8a4605be74aa9ea9d79846c1fba20a33MD52ORIGINALARTIGO_ComputingFirstEigenvalue.pdfARTIGO_ComputingFirstEigenvalue.pdfapplication/pdf286628http://www.repositorio.ufop.br/bitstream/123456789/1970/1/ARTIGO_ComputingFirstEigenvalue.pdfcc10afa1056273eda183f9aea7f18401MD51123456789/19702019-03-15 13:01:22.911oai:localhost: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Repositório InstitucionalPUBhttp://www.repositorio.ufop.br/oai/requestrepositorio@ufop.edu.bropendoar:32332019-03-15T17:01:22Repositório Institucional da UFOP - Universidade Federal de Ouro Preto (UFOP)false |
dc.title.pt_BR.fl_str_mv |
Computing the first eigenvalue of the p-Laplacian via the inverse power method. |
title |
Computing the first eigenvalue of the p-Laplacian via the inverse power method. |
spellingShingle |
Computing the first eigenvalue of the p-Laplacian via the inverse power method. Biezuner, Rodney Josué p-Laplacian First eigenvalue Comparison principle Power method |
title_short |
Computing the first eigenvalue of the p-Laplacian via the inverse power method. |
title_full |
Computing the first eigenvalue of the p-Laplacian via the inverse power method. |
title_fullStr |
Computing the first eigenvalue of the p-Laplacian via the inverse power method. |
title_full_unstemmed |
Computing the first eigenvalue of the p-Laplacian via the inverse power method. |
title_sort |
Computing the first eigenvalue of the p-Laplacian via the inverse power method. |
author |
Biezuner, Rodney Josué |
author_facet |
Biezuner, Rodney Josué Ercole, Grey Martins, Eder Marinho |
author_role |
author |
author2 |
Ercole, Grey Martins, Eder Marinho |
author2_role |
author author |
dc.contributor.author.fl_str_mv |
Biezuner, Rodney Josué Ercole, Grey Martins, Eder Marinho |
dc.subject.por.fl_str_mv |
p-Laplacian First eigenvalue Comparison principle Power method |
topic |
p-Laplacian First eigenvalue Comparison principle Power method |
description |
In this paper, we discuss a new method for computing the first Dirichlet eigenvalue of the p-Laplacian inspired by the inverse power method in finite dimensional linear algebra. The iterative technique is independent of the particular method used in solving the p-Laplacian equation and therefore can be made as efficient as the latter. The method is validated theoretically for any ball in Rn if p >1 and for any bounded domain in the particular case p = 2. For p >2 the method is validated numerically for the square. |
publishDate |
2009 |
dc.date.issued.fl_str_mv |
2009 |
dc.date.accessioned.fl_str_mv |
2012-12-05T15:50:55Z |
dc.date.available.fl_str_mv |
2012-12-05T15:50:55Z |
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.citation.fl_str_mv |
BIEZUNER, R. J.; ERCOLE, G.; MARTINS, E. M. Computing the first eigenvalue of the p-Laplacian via the inverse power method. Journal of Functional Analysis, v. 257, n. 1, p. 243-270, 2009. Disponível em: <https://www.sciencedirect.com/science/article/pii/S0022123609000445>. Acesso em: 03 dez. 2012 |
dc.identifier.uri.fl_str_mv |
http://www.repositorio.ufop.br/handle/123456789/1970 |
dc.identifier.issn.none.fl_str_mv |
00221236 |
identifier_str_mv |
BIEZUNER, R. J.; ERCOLE, G.; MARTINS, E. M. Computing the first eigenvalue of the p-Laplacian via the inverse power method. Journal of Functional Analysis, v. 257, n. 1, p. 243-270, 2009. Disponível em: <https://www.sciencedirect.com/science/article/pii/S0022123609000445>. Acesso em: 03 dez. 2012 00221236 |
url |
http://www.repositorio.ufop.br/handle/123456789/1970 |
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.source.none.fl_str_mv |
reponame:Repositório Institucional da UFOP instname:Universidade Federal de Ouro Preto (UFOP) instacron:UFOP |
instname_str |
Universidade Federal de Ouro Preto (UFOP) |
instacron_str |
UFOP |
institution |
UFOP |
reponame_str |
Repositório Institucional da UFOP |
collection |
Repositório Institucional da UFOP |
bitstream.url.fl_str_mv |
http://www.repositorio.ufop.br/bitstream/123456789/1970/2/license.txt http://www.repositorio.ufop.br/bitstream/123456789/1970/1/ARTIGO_ComputingFirstEigenvalue.pdf |
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Repositório Institucional da UFOP - Universidade Federal de Ouro Preto (UFOP) |
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repositorio@ufop.edu.br |
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