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SUMMARY:Convergence analysis of balancing principle for nonlinear Tikhonov
  regularization in Hilbert scales for statistical inverse problems - Prico
 p-Jeckstadt\, M (University of Bonn)
DTSTART:20140326T143000Z
DTEND:20140326T150000Z
UID:TALK51639@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:In this talk we focus on results regarding inverse problems de
 scribed by nonlinear operator equations both in a deterministic and statis
 tical framework. The last developments in the methodology are reviewed and
  similarities and di erences related to the nature of the setting are emph
 asized. Furthermore\, a convergence analysis leading to order optimal rate
 s 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-H
 ammerstein non-linear integral equation that has several applications as p
 opulation growth model in the population dynamics.\n\nReferences Hohage T.
  and Pricop M."Nonlinear Tikhonov regularization in Hilbert scales for inv
 erse boundary value problems with random noise".Inverse Problems and Imagi
 ng\, Vol. 2\, 271{ 290\, 2008. Bissantz N.\, Hohage T. and Munk A."Consist
 ency and rates of convergence of nonlinear Tikhonov regularization with ra
 ndom noise". Inverse Problems\, Vol. 20\, 1773{1791\, 2004.\n
LOCATION:Seminar Room 1\, Newton Institute
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