Tikhonov and Landweber convergence rates: characterization by interpolation spaces
arXiv:1503.05742
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Provides a theoretical characterization of convergence rates for regularization methods, relevant for researchers in inverse problems and functional analysis.
The paper characterizes algebraic convergence rates of Tikhonov regularization and Landweber iteration for linear inverse problems in Hilbert spaces, showing that rates correspond to the exact solution belonging to intermediate spaces from real interpolation.
Algebraic convergences rates of (iterated) Tikhonov regularization for linear inverse problems in Hilbert spaces are characterized by the membership of the exact solution to intermediate spaces produced by the K-method of real interpolation. Similar results are obtained for the Landweber iteration.