Optimal Convergence Rates Results for Linear Inverse Problems in Hilbert Spaces |
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| Authors: | V. Albani M. V. de Hoop O. Scherzer |
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| Affiliation: | 1. Computational Science Center, University of Vienna, Vienna, Austria;2. Department of Computational and Applied Mathematics and Department of Earth Science, Rice University, Houston, Texas, USA;3. Johann Radon Institute for Computational and Applied Mathematics (RICAM), Linz, Austria |
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| Abstract: | 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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| Keywords: | Approximative source conditions convergence rates linear inverse problems regularization variational source conditions |
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