Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 

 

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)

  • [1] Abstracts Amer. Math. Soc. 10 (1989), p. 235.
  • [2] 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.
  • [3] A. Erdélyi, W. Magnus, F. Oberhettinger, and F. G. Tricomi, Tables of integral transforms, Vol. 1, McGraw-Hill, New York, 1954.
  • [4] L. Gotusso, R. Pavani, and D. Roux, Numerical results from a regularization method for inversion of Fourier series, Rend. Mat. Appl. (7) 10 (1990), no. 3, 423–438. MR 1080308
  • [5] L. Gotusso and D. Roux, Teoria, analisi numerica e valutazione dei risultati di un metodo per l'inversione delle serie di Fourier, Atti Accad. Sci. Lettere Arti Palermo (to appear).
  • [6] Laura Gotusso, Delfina Roux, and Paolo Zanzi, Computation of a constant relative to a method for Fourier series inversion, Istit. Lombardo Accad. Sci. Lett. Rend. A 124 (1990), 85–98 (1991) (Italian, with English summary). MR 1267851
  • [7] V. A. Morozov, Methods for solving incorrectly posed problems, Springer-Verlag, New York, 1984. Translated from the Russian by A. B. Aries; Translation edited by Z. Nashed. MR 766231
  • [8] William H. Press, Brian P. Flannery, Saul A. Teukolsky, and William T. Vetterling, Numerical recipes, Cambridge University Press, Cambridge, 1986. The art of scientific computing. MR 833288
  • [9] Elias M. Stein and Guido Weiss, Introduction to Fourier analysis on Euclidean spaces, Princeton University Press, Princeton, N.J., 1971. Princeton Mathematical Series, No. 32. MR 0304972

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65T10

Retrieve articles in all journals with MSC: 65T10


Additional Information

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