Optimal Convergence Rates for Tikhonov Regularization in Besov Scales
نویسندگان
چکیده
Abstract. In this paper we deal with linear inverse problems and convergence rates for Tikhonov regularization. We consider regularization in a scale of Banach spaces, namely the scale of Besov spaces. We show that regularization in Banach scales differs from regularization in Hilbert scales in the sense that it is possible that stronger source conditions may lead to weaker convergence rates and vive versa. Moreover, we present optimal source conditions for regularization in Besov scales.
منابع مشابه
Necessary Conditions for Convergence Rates of Regularizations of Optimal Control Problems
We investigate the Tikhonov regularization of control constrained optimal control problems. We use a specialized source condition in combination with a condition on the active sets. In the case of high convergence rates, these conditions are necessary and sufficient.
متن کاملAdaptive regularization and discretization of bang-bang optimal control problems
In the article, Tikhonov regularization of control-constrained optimal control problems is investigated. Typically the solutions of such problems exhibit a so-called bang-bang structure. We develop a parameter choice rule that adaptively selects the Tikhonov regularization parameter depending on a-posteriori computable quantities. We prove that this choice leads to optimal convergence rates wit...
متن کاملA new approach to convergence rate analysis of Tikhonov regularization for parameter identification in heat conduction
In this paper we investigate the stability and convergence rates of the widely used output least-squares method with Tikhonov regularization for the identification of the conductivity distribution in a heat conduction system. Due to the rather restrictive source conditions and regularity assumptions on the nonlinear parameter-to-solution operator concerned, the existing Tikhonov regularization ...
متن کاملVariable Hilbert Scales and Their Interpolation Inequalities with Applications to Tikhonov Regularization
Variable Hilbert scales are constructed using the spectral theory of self-adjoint operators in Hilbert spaces. An embedding and an interpolation theorem (based on Jenssen's inequality) are proved. They generalize known results about \ordinary" Hilbert scales derived by Natterer Applic. Bounds on best possible and actual errors for regularization methods are obtained by applying the interpolatio...
متن کاملStability and Convergence Analysis of Tikhonov Regularization for Parameter Identiication in a Parabolic Equation
In this paper we investigate stability and convergence rates of the Tikhonov regularization method for the identiication of the diiusion parameter in a multi{dimensional parabolic equation. By choosing a problem{adapted approach, we obtain much better results than by applying the general theory of Tikhonov regularization of nonlinear inverse problems.
متن کامل