title: Optimal Convergence Rates Results for Linear Inverse Problems in Hilbert Spaces.
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.
authors: Computational Science Center, University of Vienna , Vienna , Austria.
authors: V
authors: V
authors: Albani
authors: Computational Science Center, University of Vienna , Vienna , Austria.
authors: P
authors: P
authors: Elbau
authors: Department of Computational and Applied Mathematics and Department of Earth Science, Rice University , Houston , Texas , USA.
authors: M V
authors: MV
authors: de Hoop
authors: Computational Science Center, University of Vienna, Vienna, Austria; Johann Radon Institute for Computational and Applied Mathematics (RICAM), Linz, Austria.
authors: O
authors: O
authors: Scherzer
keywords: 47A52; 49N45; 65J22; Approximative source conditions; convergence rates; linear inverse problems; regularization; variational source conditions