Computing

, Volume 33, Issue 3–4, pp 259–267 | Cite as

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

  • R. S. Anderssen
  • F. R. de Hoog
Contrinbuted Papers

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.

AMS Subject Classifications

65D25 62M15 

Key words

Finite difference methods numerical differentiation regularization Wiener filtering minimum variance amplification factor 

Differenzenverfahren zur numerischen Differentation fehlerbehafteter Funktionen

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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References

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Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • R. S. Anderssen
    • 1
  • F. R. de Hoog
    • 1
  1. 1.Division of Mathematics and StatisticsCSIROCanberraAustralia

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