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
Descripción
Sumario: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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