Adaptive numerical differentiation
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- by R. S. Stepleman and N. D. Winarsky PDF
- Math. Comp. 33 (1979), 1257-1264 Request permission
Abstract:
It is well known that the calculation of an accurate approximate derivative $f\prime (x)$ of a nontabular function $f(x)$ on a finite-precision computer by the formula $d(h) = (f(x + h) - f(x - h))/2h$ 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 $d(h)$ to $f\prime$, a reliable numerical method can be obtained which can yield efficiently the theoretical maximum number of accurate digits for the given machine precision.References
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Additional Information
- © Copyright 1979 American Mathematical Society
- Journal: Math. Comp. 33 (1979), 1257-1264
- MSC: Primary 65D25
- DOI: https://doi.org/10.1090/S0025-5718-1979-0537969-8
- MathSciNet review: 537969