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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
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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    Abstracts Amer. Math. Soc. 10 (1989), p. 235. L. De Michele, M. Di Natale, and D. Roux, Sharp properties of a regularization method for inversion of Fourier series, Proc. Meeting "Trends in Functional Analysis and Approximation Theory," Atti Sem. Mat. Fis. Univ. Modena 39 (1991), 253-267. A. Erdélyi, W. Magnus, F. Oberhettinger, and F. G. Tricomi, Tables of integral transforms, Vol. 1, McGraw-Hill, New York, 1954.
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Article copyright: © Copyright 1992 American Mathematical Society