The Halpern-Mann iteration in CAT(0) spaces.
Autor(a) principal: | |
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Data de Publicação: | 2022 |
Tipo de documento: | Artigo de conferência |
Idioma: | por |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10174/33646 |
Resumo: | Complete CAT(0) spaces, also known as Hadamard spaces, are a non-linear generalization of Hilbert spaces. Benefiting from ideas and tools from the proof mining program it was shown by Dinis and Pinto the strong convergence of an iterative schema which alternates between Halpern and Krasnoselskii-Mann style iterations in the general context of CAT(0) spaces. At the same time, the logical tools used allowed to obtain quantitative information in the form of rates of asymptotic regularity and rates of metastability (in the sense of T. Tao). If one restricts oneself to Hilbert spaces, the proof follows some standard arguments. However, to obtain the proof in the more general context of CAT(0) spaces the use of logical tools, and in particular the technique introduced by Ferreira et al., seem to be necessary. In this talk I will explain the role of the logical tools in obtaining this result. |
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The Halpern-Mann iteration in CAT(0) spaces.Proof miningHalpern-Mann iterationCAT(0) spacesComplete CAT(0) spaces, also known as Hadamard spaces, are a non-linear generalization of Hilbert spaces. Benefiting from ideas and tools from the proof mining program it was shown by Dinis and Pinto the strong convergence of an iterative schema which alternates between Halpern and Krasnoselskii-Mann style iterations in the general context of CAT(0) spaces. At the same time, the logical tools used allowed to obtain quantitative information in the form of rates of asymptotic regularity and rates of metastability (in the sense of T. Tao). If one restricts oneself to Hilbert spaces, the proof follows some standard arguments. However, to obtain the proof in the more general context of CAT(0) spaces the use of logical tools, and in particular the technique introduced by Ferreira et al., seem to be necessary. In this talk I will explain the role of the logical tools in obtaining this result.2023-01-25T15:37:21Z2023-01-252022-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/conferenceObjecthttp://hdl.handle.net/10174/33646http://hdl.handle.net/10174/33646porhttps://daysinlogic2022.ualg.pt/simnaonaoCIMAbruno.dinis@uevora.ptDinis, Brunoinfo:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2024-01-03T19:35:34Zoai:dspace.uevora.pt:10174/33646Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T01:22:24.013669Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse |
dc.title.none.fl_str_mv |
The Halpern-Mann iteration in CAT(0) spaces. |
title |
The Halpern-Mann iteration in CAT(0) spaces. |
spellingShingle |
The Halpern-Mann iteration in CAT(0) spaces. Dinis, Bruno Proof mining Halpern-Mann iteration CAT(0) spaces |
title_short |
The Halpern-Mann iteration in CAT(0) spaces. |
title_full |
The Halpern-Mann iteration in CAT(0) spaces. |
title_fullStr |
The Halpern-Mann iteration in CAT(0) spaces. |
title_full_unstemmed |
The Halpern-Mann iteration in CAT(0) spaces. |
title_sort |
The Halpern-Mann iteration in CAT(0) spaces. |
author |
Dinis, Bruno |
author_facet |
Dinis, Bruno |
author_role |
author |
dc.contributor.author.fl_str_mv |
Dinis, Bruno |
dc.subject.por.fl_str_mv |
Proof mining Halpern-Mann iteration CAT(0) spaces |
topic |
Proof mining Halpern-Mann iteration CAT(0) spaces |
description |
Complete CAT(0) spaces, also known as Hadamard spaces, are a non-linear generalization of Hilbert spaces. Benefiting from ideas and tools from the proof mining program it was shown by Dinis and Pinto the strong convergence of an iterative schema which alternates between Halpern and Krasnoselskii-Mann style iterations in the general context of CAT(0) spaces. At the same time, the logical tools used allowed to obtain quantitative information in the form of rates of asymptotic regularity and rates of metastability (in the sense of T. Tao). If one restricts oneself to Hilbert spaces, the proof follows some standard arguments. However, to obtain the proof in the more general context of CAT(0) spaces the use of logical tools, and in particular the technique introduced by Ferreira et al., seem to be necessary. In this talk I will explain the role of the logical tools in obtaining this result. |
publishDate |
2022 |
dc.date.none.fl_str_mv |
2022-01-01T00:00:00Z 2023-01-25T15:37:21Z 2023-01-25 |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/conferenceObject |
format |
conferenceObject |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/10174/33646 http://hdl.handle.net/10174/33646 |
url |
http://hdl.handle.net/10174/33646 |
dc.language.iso.fl_str_mv |
por |
language |
por |
dc.relation.none.fl_str_mv |
https://daysinlogic2022.ualg.pt/ sim nao nao CIMA bruno.dinis@uevora.pt |
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info:eu-repo/semantics/openAccess |
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openAccess |
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Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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RCAAP |
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RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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1799136705621524480 |