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Finite difference methods for the numerical differentiation of non-exact data

Differenzenverfahren zur numerischen Differentation fehlerbehafteter Funktionen

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Abstract

In this paper, we derive results about the numerical performance of multi-point (moving average) finite difference formulas for the differentiation of non-exact data. In particular, we show that multi-point differentiators can be constructed which are asymptotically unbiased and have a bounded amplification factor as the steplength decreases and the number of points increases.

Zusammenfassung

In dieser Arbeit werden Ergebnisse über die numerische Güte von Mehrpunktdifferenzenformeln für die Differentation empirischer Funktionen hergeleitet. Insbesondere wird gezeigt, daß Mehrpunktdifferenzenoperatoren konstruiert werden können, die asymptotisch verzerrungsfrei sind und einen für abnehmende Schrittweite und zunehmende Punkteanzahl beschränkten Amplifikationsfaktor besitzen.

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Authors and Affiliations

  1. Division of Mathematics and Statistics, CSIRO, GPO Box 1965, 2601, Canberra, ACT, Australia

    R. S. Anderssen & F. R. de Hoog

Authors
  1. R. S. Anderssen
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  2. F. R. de Hoog
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Additional information

Dedicated to Professor Karl Nickel on the occasion of his 60th birthday.

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Anderssen, R.S., de Hoog, F.R. Finite difference methods for the numerical differentiation of non-exact data. Computing 33, 259–267 (1984). https://doi.org/10.1007/BF02242272

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  • DOI: https://doi.org/10.1007/BF02242272

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