Adaptive numerical differentiation

Authors:
R. S. Stepleman and N. D. Winarsky

Journal:
Math. Comp. **33** (1979), 1257-1264

MSC:
Primary 65D25

DOI:
https://doi.org/10.1090/S0025-5718-1979-0537969-8

MathSciNet review:
537969

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Abstract: It is well known that the calculation of an accurate approximate derivative of a nontabular function on a finite-precision computer by the formula is a delicate task. If *h* is too large, truncation errors cause poor answers, while if *h* is too small, cancellation and other "rounding" errors cause poor answers. We will show that by using simple results on the nature of the asymptotic convergence of to , a reliable numerical method can be obtained which can yield efficiently the theoretical maximum number of accurate digits for the given machine precision.

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DOI:
https://doi.org/10.1090/S0025-5718-1979-0537969-8

Article copyright:
© Copyright 1979
American Mathematical Society