Abstract
In this work we determine the normal solution of the finite moment problem in three different Hilbert space settings, both in the absence and in the presence of noisy data. In two cases the normal solution is a polynomial while in the third it is not. However, in each case the normal solution is spanned by orthogonal functions that are obtained by computationally efficient algorithms. A criterion of “a posteriori validation”, to select that normal solution which minimizes the uniform norm of the recovery error, is also given. The effectiveness of the method is illustrated with a number of test functions, for the most part already proposed in the literature.
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Rodriguez, G., Seatzu, S. Approximation methods for the finite moment problem. Numer Algor 5, 391–405 (1993). https://doi.org/10.1007/BF02109420
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DOI: https://doi.org/10.1007/BF02109420