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SUMMARY:Linearised inverse conductivity problem: reconstruction and Lipsch
 itz stability for infinite-dimensional spaces of perturbations - Nuutti Hy
 vönen (Aalto University)
DTSTART:20230328T085000Z
DTEND:20230328T094000Z
UID:TALK198214@talks.cam.ac.uk
DESCRIPTION:The linearised inverse conductivity problem is investigated in
  a two-dimensional bounded simply connected domain with a smooth enough bo
 undary. After extending the linearised problem for square integrable pertu
 rbations\, the space of perturbations is orthogonally decomposed and Lipsc
 hitz stability\, with explicit Lipschitz constants\, is proven for each of
  the infinite-dimensional subspaces. The stability estimates are based on 
 using the Hilbert-Schmidt norm for the Neumann-to-Dirichlet boundary map a
 nd its Fr{\\'e}chet derivative with respect to the conductivity coefficien
 t. A direct reconstruction method that inductively yields the orthogonal p
 rojections of a conductivity coefficient onto the aforementioned subspaces
  is devised and numerically tested with data simulated by solving the orig
 inal nonlinear forward problem.
LOCATION:Seminar Room 1\, Newton Institute
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