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- W3010878089 abstract "In this paper, we analyze the convergence rates of well known Tikhonov regularization scheme for solving the nonlinear ill-posed problems by incorporating the conditional stability estimates. In particular, we obtain the convergence rates via two different approaches. The first approach is the standard one via Bregman distances and the second one is in terms of 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. Moreover, a novel smoothness condition is introduced termed as approximate Holder stability estimates, which is further exploited to obtain the convergence rates. We also discuss the convergence rates for Tikhonov regularization with sparsity constraints by incorporating the conditional stability estimates. At the end, some examples are given to complement the abstract theory." @default.
- W3010878089 created "2020-03-23" @default.
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- W3010878089 date "2018-05-30" @default.
- W3010878089 modified "2023-09-27" @default.
- W3010878089 title "Convergence rates of nonlinear inverse problems in Banach spaces: Conditional stability and approximation of Hölder stability" @default.
- W3010878089 hasPublicationYear "2018" @default.
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