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On the choice of parameter in a method for the inversion of Fourier series


Authors: M. Di Natale, L. Gotusso, R. Pavani and D. Roux
Journal: Math. Comp. 58 (1992), 737-744
MSC: Primary 65T10
DOI: https://doi.org/10.1090/S0025-5718-1992-1122063-4
MathSciNet review: 1122063
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Abstract: The a priori evaluation of the pointwise approximation, by a regularization method suggested earlier, of a $ {L^1}$ periodic function f, when only noisy Fourier coefficients of f are known, is given here in a formulation more suitable for numerical verification. A careful evaluation of the constants involved in the formulas is also provided. Finally, a procedure is described of a statistical check performed in order to verify whether the theoretically suggested value of the regularization parameter is a good choice with respect to functions generally arising in applications.


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DOI: https://doi.org/10.1090/S0025-5718-1992-1122063-4
Article copyright: © Copyright 1992 American Mathematical Society