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A stable finite difference ansatz for higher order differentiation of non-exact data

Published online by Cambridge University Press:  17 April 2009

Bob Anderssen ,
Frank de Hoog  and
Markus Hegland
Bob Anderssen
Affiliation:
Division of Mathematics and Statistics, CSIRO, GPO Box 1965, Canberra ACT 2601, Australia
Frank de Hoog
Affiliation:
Division of Mathematics and Statistics, CSIRO, GPO Box 1965, Canberra ACT 2601, Australia
Markus Hegland
Affiliation:
Computer Sciences Laboratory, RSISE, Australian National University, Canberra ACT 0200, Australia
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Abstract

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If standard central difference formulas are used to compute second or third order derivatives from measured data even quite precise data can lead to totally unusable results due to the basic instability of the differentiation process. Here an averaging procedure is presented and analysed which allows the stable computation of low order derivatives from measured data. The new method first averages the data, then samples the averages and finally applies standard difference formulas. The size of the averaging set acts like a regularisation parameter and has to be chosen as a function of the grid size h.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 58 , Issue 2 , October 1998 , pp. 223 - 232
Copyright
Copyright © Australian Mathematical Society 1998

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