Data Based Regularization Matrices for the Tikhonov-Phillips Regularization
نویسندگان
چکیده
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 ‖Lx‖2 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 ‖LkD x̃ x‖2 where the diagonal matrix Dx̃ := diag(|x̃1|, . . . , |x̃n|) and x̃ is the best available approximate solution to x.
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