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OPTIMAL CONVERGENCE RATES FOR TIKHONOV REGULARIZATION IN BESOV SPACES.
- Source :
-
SIAM Journal on Numerical Analysis . 2020, Vol. 58 Issue 1, p21-47. 27p. - Publication Year :
- 2020
-
Abstract
- This paper deals with Tikhonov regularization for linear and nonlinear ill-posed operator equations with wavelet Besov norm penalties. We show order optimal rates of convergence for finitely smoothing operators and for the backwards heat equation for a range of Besov spaces using variational source conditions. We also derive order optimal rates for a white noise model with the help of variational source conditions and concentration inequalities for sharp negative Besov norms of the noise. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00361429
- Volume :
- 58
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- SIAM Journal on Numerical Analysis
- Publication Type :
- Academic Journal
- Accession number :
- 144779583
- Full Text :
- https://doi.org/10.1137/18M1178098