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Convergence of a reconstruction method for the inverse conductivity problem. (English) Zbl 0747.35051
Summary: The inverse conductivity problem is that of reconstructing a spatially varying isotropic conductivity in the interior of some region by means of steady-state measurements taken at the boundary. Reconstruction schemes including least-squares type minimization methods have been widely studied and implemented, but convergence analysis has been largely ignored. This paper establishes the convergence of a well-known least- squares minimization scheme — the Levenberg-Marquard method — on a regularized formulation of the inverse conductivity problem.

MSC:
35R30Inverse problems for PDE
49M15Newton-type methods in calculus of variations
65K10Optimization techniques (numerical methods)