Optimal Convergence Rates Results for Linear Inverse Problems in Hilbert Spaces

In this article, we prove optimal convergence rates results for regularization methods for solving linear ill-posed operator equations in Hilbert spaces. The results generalizes existing convergence rates results on optimality to general source conditions, such as logarithmic source conditions. More...

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Detalles Bibliográficos
Autores principales: Albani, V., Elbau, P., de Hoop, M. V., Scherzer, O.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Taylor & Francis 2016
Materias:
Original Articles
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4959128/
https://www.ncbi.nlm.nih.gov/pubmed/27499565
http://dx.doi.org/10.1080/01630563.2016.1144070
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author Albani, V.
Elbau, P.
de Hoop, M. V.
Scherzer, O.
author_facet Albani, V.
Elbau, P.
de Hoop, M. V.
Scherzer, O.
author_sort Albani, V.
collection PubMed
description In this article, we prove optimal convergence rates results for regularization methods for solving linear ill-posed operator equations in Hilbert spaces. The results generalizes existing convergence rates results on optimality to general source conditions, such as logarithmic source conditions. Moreover, we also provide optimality results under variational source conditions and show the connection to approximative source conditions.
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spelling pubmed-49591282016-08-05 Optimal Convergence Rates Results for Linear Inverse Problems in Hilbert Spaces Albani, V. Elbau, P. de Hoop, M. V. Scherzer, O. Numer Funct Anal Optim Original Articles In this article, we prove optimal convergence rates results for regularization methods for solving linear ill-posed operator equations in Hilbert spaces. The results generalizes existing convergence rates results on optimality to general source conditions, such as logarithmic source conditions. Moreover, we also provide optimality results under variational source conditions and show the connection to approximative source conditions. Taylor & Francis 2016-02-02 2016-02-08 /pmc/articles/PMC4959128/ /pubmed/27499565 http://dx.doi.org/10.1080/01630563.2016.1144070 Text en Published with license by Taylor & Francis http://creativecommons.org/licenses/by-nc-nd/4.0/legalcode This is an Open Access article. Non-commercial re-use, distribution, and reproduction in any medium, provided the original work is properly attributed, cited, and is not altered, transformed, or built upon in any way, is permitted. The moral rights of the named author(s) have been asserted.
spellingShingle Original Articles
Albani, V.
Elbau, P.
de Hoop, M. V.
Scherzer, O.
Optimal Convergence Rates Results for Linear Inverse Problems in Hilbert Spaces
title Optimal Convergence Rates Results for Linear Inverse Problems in Hilbert Spaces
title_full Optimal Convergence Rates Results for Linear Inverse Problems in Hilbert Spaces
title_fullStr Optimal Convergence Rates Results for Linear Inverse Problems in Hilbert Spaces
title_full_unstemmed Optimal Convergence Rates Results for Linear Inverse Problems in Hilbert Spaces
title_short Optimal Convergence Rates Results for Linear Inverse Problems in Hilbert Spaces
title_sort optimal convergence rates results for linear inverse problems in hilbert spaces
topic Original Articles
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4959128/
https://www.ncbi.nlm.nih.gov/pubmed/27499565
http://dx.doi.org/10.1080/01630563.2016.1144070
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