Optimal order of accuracy in Vasin's method for differentiation of noisy functions

  • C. W. Groetsch
Technical Note

Abstract

We improve the order of accuracy estimate for Vasin's method for approximate differentiation. The improved estimate is shown to be the best possible.

Key Words

Smoothing approximate differentiation order of accuracy error level 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Vasin, V. V.,The Stable Evaluationof a Derivative in the Space C(-∞, ∞), USSR Computational Mathematics and Mathematical Physics, Vol. 13, pp. 16–24, 1973.Google Scholar
  2. 2.
    Murio, D. A.,Automatic Numerical Differentiation by Discrete Mollification, Computers and Mathematics with Applications, Vol. 13, pp. 381–386, 1987.Google Scholar
  3. 3.
    Hamming, R.,Digital Filters, Prentice-Hall, Englewood Cliffs, New Jersey, 1977.Google Scholar
  4. 4.
    Anderssen, R. S., andBloomfield, P.,Numerical Differentiation Procedures for Nonexact Data, Numerisch Mathematik, Vol. 22, pp. 157–182, 1974.Google Scholar
  5. 5.
    Lancoz, C.,Applied Analysis, Prentice-Hall, Englewood Cliffs, New Jersey, 1956.Google Scholar
  6. 6.
    Cullum, J.,Numerical Differentiation and Regularization, SIAM Journal on Numerical Analysis, Vol. 8, pp. 254–265, 1971.Google Scholar
  7. 7.
    King, J. T., andMurio, D. A.,Numerical Differentiation by Finite-Dimensional Regularization, IMA Journal of Numerical Analysis, Vol. 6, pp. 65–85, 1986.Google Scholar
  8. 8.
    Sobolev, S. L.,Einige Anwendungen der Funktionalanalysis auf Gleichungen der Mathematischen Physik, Akademic Verlag, Berlin, Germany, 1964.Google Scholar
  9. 9.
    Groetsch, C. W.,The Theory of Tikhonov Regularization for Fredholm Equations of the First Kind, Pitman, London, England, 1984.Google Scholar
  10. 10.
    Groetsch, C. W.,Differentiation of Approximately Specified Functions, American Mathematical Monthly, Vol. 98, pp. 847–850, 1991.Google Scholar

Copyright information

© Plenum Publishing Corporation 1992

Authors and Affiliations

  • C. W. Groetsch
    • 1
  1. 1.Department of Mathematical SciencesUniversity of CincinnatiCincinnati

Personalised recommendations