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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

On the choice of parameter in a method for the inversion of Fourier series
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by M. Di Natale, L. Gotusso, R. Pavani and D. Roux PDF
Math. Comp. 58 (1992), 737-744 Request permission

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
    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.
  • 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
  • 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).
  • 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
  • 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, DOI 10.1007/978-1-4612-5280-1
  • 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
  • Elias M. Stein and Guido Weiss, Introduction to Fourier analysis on Euclidean spaces, Princeton Mathematical Series, No. 32, Princeton University Press, Princeton, N.J., 1971. MR 0304972
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Additional Information
  • © Copyright 1992 American Mathematical Society
  • Journal: Math. Comp. 58 (1992), 737-744
  • MSC: Primary 65T10
  • DOI: https://doi.org/10.1090/S0025-5718-1992-1122063-4
  • MathSciNet review: 1122063