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math.OC2011
Variational Inequalities and Improved Convergence Rates for Tikhonov Regularisation on Banach Spaces
Markus Grasmair
In this paper we derive higher order convergence rates in terms of the Bregman distance for Tikhonov like convex regularisation for linear operator equations on Banach spaces. The…
math.OC2011
An Approach to the Minimization of the Mumford-Shah Functional using Γ-convergence and Topological Asymptotic Expansion
Markus Grasmair, Monika Muszkieta, Otmar Scherzer
In this paper, we present a method for the numerical minimization of the Mumford-Shah functional that is based on the idea of topological asymptotic expansions. The basic idea is t…