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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Convergence analysis of balancing principle for no
nlinear Tikhonov regularization in Hilbert scales
for statistical inverse problems - Pricop-Jeckstad
t\, M (University of Bonn)
DTSTART;TZID=Europe/London:20140326T143000
DTEND;TZID=Europe/London:20140326T150000
UID:TALK51639AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/51639
DESCRIPTION:In this talk we focus on results regarding inverse
problems described by nonlinear operator equation
s both in a deterministic and statistical framewor
k. The last developments in the methodology are re
viewed and similarities and di erences related to
the nature of the setting are emphasized. Furtherm
ore\, a convergence analysis leading to order opti
mal rates in the deterministic case and order-opti
mal rates up to a log-factor in the stochastic cas
e for the Lepskii choice of the regularization par
ameter for a range of smoothness classes and with
a milder smallness assumptions is presented. These
assumptions are shown to be satisfied by a Volter
ra-Hammerstein non-linear integral equation that h
as several applications as population growth model
in the population dynamics.\n\nReferences Hohage
T. and Pricop M."Nonlinear Tikhonov regularization
in Hilbert scales for inverse boundary value prob
lems with random noise".Inverse Problems and Imagi
ng\, Vol. 2\, 271{ 290\, 2008. Bissantz N.\, Hohag
e T. and Munk A."Consistency and rates of converge
nce of nonlinear Tikhonov regularization with rand
om noise". Inverse Problems\, Vol. 20\, 1773{1791\
, 2004.\n
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:Mustapha Amrani
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