Solving an abstract nonlinear eigenvalue problem by the inverse iteration method

Detalhes bibliográficos
Autor(a) principal: Grey Ercole
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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spelling 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
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 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
dc.source.none.fl_str_mv reponame:Repositório Institucional da UFMG
instname:Universidade Federal de Minas Gerais (UFMG)
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instname_str Universidade Federal de Minas Gerais (UFMG)
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reponame_str Repositório Institucional da UFMG
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