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Abstract

In Tikhonov-Phillips regularization of general form the given ill-posed linear system is replaced by a Least Squares problem including a minimization of the solution vector x, relative to a seminorm equation image with some regularization matrix L. Based on the finite difference matrix Lk, given by a discretization of the first or second derivative, we introduce the seminorm equation image where the diagonal matrix equation image and equation image is the best available approximate solution to x. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)