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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Linearised inverse conductivity problem: reconstru
ction and Lipschitz stability for infinite-dimensi
onal spaces of perturbations - Nuutti Hyvönen (Aal
to University)
DTSTART;TZID=Europe/London:20230328T095000
DTEND;TZID=Europe/London:20230328T104000
UID:TALK198214AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/198214
DESCRIPTION:The linearised inverse conductivity problem is inv
estigated in a two-dimensional bounded simply conn
ected domain with a smooth enough boundary. After
extending the linearised problem for square integr
able perturbations\, the space of perturbations is
orthogonally decomposed and Lipschitz stability\,
with explicit Lipschitz constants\, is proven for
each of the infinite-dimensional subspaces. The s
tability estimates are based on using the Hilbert-
Schmidt norm for the Neumann-to-Dirichlet boundary
map and its Fr{\\'e}chet derivative with respect
to the conductivity coefficient. A direct reconstr
uction method that inductively yields the orthogon
al projections of a conductivity coefficient onto
the aforementioned subspaces is devised and numeri
cally tested with data simulated by solving the or
iginal nonlinear forward problem.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:
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