Solving an abstract nonlinear eigenvalue problem by the inverse iteration method
Autor(a) principal: | |
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Data de Publicação: | 2018 |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UFMG |
Texto Completo: | https://doi.org/10.1007/s00574-018-0070-3 http://hdl.handle.net/1843/37403 https://orcid.org/0000-0002-0459-7292 |
Resumo: | Let (X,‖·‖X) and (Y, ‖·‖ Y) be Banach spaces over R, with X uniformly convex and compactly embedded into Y. The inverse iteration method is applied tosolve the abstract eigenvalue problem A (w) = λ ‖ w ‖ p−q Y B (w), where the maps A: X→X and B: Y→Y are homogeneous of degreesp−1 and q−1, respectively. |
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2021-08-10T23:34:59Z2021-08-10T23:34:59Z2018-09493577591https://doi.org/10.1007/s00574-018-0070-31678-7544 (print) 1678-7714 (web)http://hdl.handle.net/1843/37403https://orcid.org/0000-0002-0459-7292Let (X,‖·‖X) and (Y, ‖·‖ Y) be Banach spaces over R, with X uniformly convex and compactly embedded into Y. The inverse iteration method is applied tosolve the abstract eigenvalue problem A (w) = λ ‖ w ‖ p−q Y B (w), where the maps A: X→X and B: Y→Y are homogeneous of degreesp−1 and q−1, respectively.Sejam (X, ‖ · ‖X) e (Y, ‖ · ‖ Y) espaços de Banach sobre R, com X uniformemente convexo e compactamente embutido em Y. O método de iteração inversa é aplicado para resolver o problema de autovalor abstrato A (w) = λ ‖ w ‖ p − q YB (w), onde os mapas A: X → X e B: Y → Y são homogêneos de graus p − 1 e q − 1, respectivamente.CNPq - Conselho Nacional de Desenvolvimento Científico e TecnológicoFAPEMIG - Fundação de Amparo à Pesquisa do Estado de Minas GeraisengUniversidade Federal de Minas GeraisUFMGBrasilICX - DEPARTAMENTO DE MATEMÁTICABulletin of the Brazilian Mathematical SocietyAutovaloresMatriz inversaEquações diferenciais elípticasMétodos iterativos (Matemática)Eigenvalue problemsInverse iterationQuasilinear elliptic equationsSolving an abstract nonlinear eigenvalue problem by the inverse iteration methodResolvendo um problema abstrato de autovalor não linear pelo método de iteração inversainfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttps://link.springer.com/article/10.1007/s00574-018-0070-3Grey Ercoleapplication/pdfinfo:eu-repo/semantics/openAccessreponame:Repositório Institucional da UFMGinstname:Universidade Federal de Minas Gerais (UFMG)instacron:UFMGLICENSELicense.txtLicense.txttext/plain; charset=utf-82042https://repositorio.ufmg.br/bitstream/1843/37403/1/License.txtfa505098d172de0bc8864fc1287ffe22MD51ORIGINALMAT _ Ercole Grey _Solving an Abstract Nonlinear Eigenvalue Problem by the Inverse Iteration Method _2018.pdfMAT _ Ercole Grey _Solving an Abstract Nonlinear Eigenvalue Problem by the Inverse Iteration Method _2018.pdfapplication/pdf7481115https://repositorio.ufmg.br/bitstream/1843/37403/2/MAT%20_%20Ercole%20Grey%20_Solving%20an%20Abstract%20Nonlinear%20Eigenvalue%20Problem%20by%20the%20Inverse%20Iteration%20Method%20_2018.pdf245624aa0f77e0c1a98b351fa6bb298bMD521843/374032021-08-10 20:34:59.776oai:repositorio.ufmg.br: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Repositório de PublicaçõesPUBhttps://repositorio.ufmg.br/oaiopendoar:2021-08-10T23:34:59Repositório Institucional da UFMG - Universidade Federal de Minas Gerais (UFMG)false |
dc.title.pt_BR.fl_str_mv |
Solving an abstract nonlinear eigenvalue problem by the inverse iteration method |
dc.title.alternative.pt_BR.fl_str_mv |
Resolvendo um problema abstrato de autovalor não linear pelo método de iteração inversa |
title |
Solving an abstract nonlinear eigenvalue problem by the inverse iteration method |
spellingShingle |
Solving an abstract nonlinear eigenvalue problem by the inverse iteration method Grey Ercole Eigenvalue problems Inverse iteration Quasilinear elliptic equations Autovalores Matriz inversa Equações diferenciais elípticas Métodos iterativos (Matemática) |
title_short |
Solving an abstract nonlinear eigenvalue problem by the inverse iteration method |
title_full |
Solving an abstract nonlinear eigenvalue problem by the inverse iteration method |
title_fullStr |
Solving an abstract nonlinear eigenvalue problem by the inverse iteration method |
title_full_unstemmed |
Solving an abstract nonlinear eigenvalue problem by the inverse iteration method |
title_sort |
Solving an abstract nonlinear eigenvalue problem by the inverse iteration method |
author |
Grey Ercole |
author_facet |
Grey Ercole |
author_role |
author |
dc.contributor.author.fl_str_mv |
Grey Ercole |
dc.subject.por.fl_str_mv |
Eigenvalue problems Inverse iteration Quasilinear elliptic equations |
topic |
Eigenvalue problems Inverse iteration Quasilinear elliptic equations Autovalores Matriz inversa Equações diferenciais elípticas Métodos iterativos (Matemática) |
dc.subject.other.pt_BR.fl_str_mv |
Autovalores Matriz inversa Equações diferenciais elípticas Métodos iterativos (Matemática) |
description |
Let (X,‖·‖X) and (Y, ‖·‖ Y) be Banach spaces over R, with X uniformly convex and compactly embedded into Y. The inverse iteration method is applied tosolve the abstract eigenvalue problem A (w) = λ ‖ w ‖ p−q Y B (w), where the maps A: X→X and B: Y→Y are homogeneous of degreesp−1 and q−1, respectively. |
publishDate |
2018 |
dc.date.issued.fl_str_mv |
2018-09 |
dc.date.accessioned.fl_str_mv |
2021-08-10T23:34:59Z |
dc.date.available.fl_str_mv |
2021-08-10T23:34:59Z |
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/1843/37403 |
dc.identifier.doi.pt_BR.fl_str_mv |
https://doi.org/10.1007/s00574-018-0070-3 |
dc.identifier.issn.pt_BR.fl_str_mv |
1678-7544 (print) 1678-7714 (web) |
dc.identifier.orcid.pt_BR.fl_str_mv |
https://orcid.org/0000-0002-0459-7292 |
url |
https://doi.org/10.1007/s00574-018-0070-3 http://hdl.handle.net/1843/37403 https://orcid.org/0000-0002-0459-7292 |
identifier_str_mv |
1678-7544 (print) 1678-7714 (web) |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.ispartof.pt_BR.fl_str_mv |
Bulletin of the Brazilian Mathematical Society |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
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openAccess |
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application/pdf |
dc.publisher.none.fl_str_mv |
Universidade Federal de Minas Gerais |
dc.publisher.initials.fl_str_mv |
UFMG |
dc.publisher.country.fl_str_mv |
Brasil |
dc.publisher.department.fl_str_mv |
ICX - DEPARTAMENTO DE MATEMÁTICA |
publisher.none.fl_str_mv |
Universidade Federal de Minas Gerais |
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