Ankik Kumar Giri, Gaurav Mittal
Published 2018-05-30Version 1
In this paper, we analyze the convergence rates of Tikhonov regularization for solving the nonlinear ill-posed problems by using the Holder stability estimates as the smoothness condition. We obtain the convergence rates via two different approaches. The first approach is the standard one which is to obtain the convergence rates in terms of Bregman distance and the second one is to obtain the convergence rates in weaker norms. The important aspect in the second approach is that the regularization is only used to constrain the regularized solutions to a set where stability holds.
An iteration regularizaion method with general convex penalty for nonlinear inverse problems in Banach spaces
Convergence rates for linear and nonlinear inverse problems in Hilbert spaces via Holder stability estimates
Convergence rates in $\ell^1$-regularization when the basis is not smooth enough
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