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Convergence rates of nonlinear inverse problems in Banach spaces: conditional stability and weaker norms

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arxiv 1805.11854 v5 pith:WN56NFE7 submitted 2018-05-30 math.NA cs.NA

classification math.NAcs.NA
keywords convergenceproblemsratesbanachconditionalill-posedinversenonlinear
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In this short note, we formulate the convergence rates of the well known Tikhonov regularization scheme for solving the nonlinear ill-posed problems in Banach spaces. For deriving the convergence rates, we employ the novel smoothness concept of conditional stability estimates in terms of weaker norms. Moreover, we show that our results are applicable on two ill-posed inverse problems.

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