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Variational smoothness assumptions in convergence rate theory—an overview
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Jens Flemming
Published/Copyright:
June 5, 2013
Abstract.
Variational smoothness assumptions are a concept for measuring abstract smoothness of solutions to operator equations. Such assumptions are useful for analyzing regularization methods, especially for proving convergence rates in Banach spaces and in more general settings. We collect results from different papers published by several authors during the last five years. The aim is to present an overview of this relatively new concept to the interested reader without going too deep into the details.
Keywords: Nonlinear ill-posed problems; Tikhonov regularization; convergence rates; smoothness assumptions
Received: 2012-10-01
Published Online: 2013-06-05
Published in Print: 2013-06-01
© 2013 by Walter de Gruyter Berlin Boston
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Keywords for this article
Nonlinear ill-posed problems;
Tikhonov regularization;
convergence rates;
smoothness assumptions
Articles in the same Issue
- Masthead
- “Recent Progress in Regularization Theory” Minisymposium M5 of the 6-th International Conference “Inverse Problems: Modeling and Simulation”
- TGV for diffusion tensors: A comparison of fidelity functions
- Variational inequalities and higher order convergence rates for Tikhonov regularisation on Banach spaces
- Variational smoothness assumptions in convergence rate theory—an overview
- On the smoothness and convexity of Besov spaces
- An H1-Kaczmarz reconstructor for atmospheric tomography
- A new cumulative wavefront reconstructor for the Shack–Hartmann sensor
