Applied and computational complex analysis. Vol. 3: discrete Fourier analysis—Cauchy integrals—construction of conformal maps---univalent functions
Pade´, stable Pade´, and Chebyshev-Pade´ approximation
Algorithms for approximation
Linear sampling methods for inverse boundary value problems in potential theory
Applied Numerical Mathematics
Convex backscattering support in electric impedance tomography
Numerische Mathematik
Electrostatic backscattering by insulating obstacles
Journal of Computational and Applied Mathematics
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This paper investigates backscatter data for the inverse obstacle problem in impedance tomography, when the obstacles are small. It is shown that under this circumstance the backscatter data are close approximations of a rational function that has second or fourth order poles at the locations of the obstacles. Furthermore, a numerical method is presented to locate the obstacles via the poles of certain Laurent-Padé approximations. Numerical experiments explore the potential of this algorithm also for extended obstacles, taking into consideration that the problem is severely ill-posed.