University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > Convergence analysis of balancing principle for nonlinear Tikhonov regularization in Hilbert scales for statistical inverse problems

Convergence analysis of balancing principle for nonlinear Tikhonov regularization in Hilbert scales for statistical inverse problems

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Mathematical, Statistical and Computational Aspects of the New Science of Metagenomics

In this talk we focus on results regarding inverse problems described by nonlinear operator equations both in a deterministic and statistical framework. The last developments in the methodology are reviewed and similarities and di erences related to the nature of the setting are emphasized. Furthermore, a convergence analysis leading to order optimal rates in the deterministic case and order-optimal rates up to a log-factor in the stochastic case for the Lepskii choice of the regularization parameter for a range of smoothness classes and with a milder smallness assumptions is presented. These assumptions are shown to be satisfied by a Volterra-Hammerstein non-linear integral equation that has several applications as population growth model in the population dynamics.

References Hohage T. and Pricop M.”Nonlinear Tikhonov regularization in Hilbert scales for inverse boundary value problems with random noise”.Inverse Problems and Imaging, Vol. 2, 271{ 290, 2008. Bissantz N., Hohage T. and Munk A.”Consistency and rates of convergence of nonlinear Tikhonov regularization with random noise”. Inverse Problems, Vol. 20, 1773{1791, 2004.

This talk is part of the Isaac Newton Institute Seminar Series series.

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