The a priori evaluation of the pointwise approximation, by a regularization method suggested earlier, of a L1periodic 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
DI NATALE, M., Gotusso, L., Pavani, R., Roux, D. (1992). On the choice of parameter in a method for the inversion of Fourier series. MATHEMATICS OF COMPUTATION, 58(198), 737-744 [10.1090/S0025-5718-1992-1122063-4].
On the choice of parameter in a method for the inversion of Fourier series
DI NATALE, MARINA;
1992
Abstract
The a priori evaluation of the pointwise approximation, by a regularization method suggested earlier, of a L1periodic 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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