Published December 1981
| public
Journal Article
Numerical Differentiation of Analytic Functions
- Creators
- Fornberg, Bengt
Abstract
It is well known that the classical difference formulas for evaluating high derivatives of a real function f(ζ) are very ill-conditioned. However, if the function f(ζ) is analytic and can be evaluated for complex values of ζ, the problem can be shown to be perfectly well-conditioned. An algorithm that performs this evaluation for an arbitrary analytic function f(~) is described. A short FORTRAN program for generating up to 50 leading derivatives is to be found in the algorithm section of this issue. To use this program, no knowledge is required either of the method or of the analytical nature (e.g., position of nearest singularity, its type) of the function.
Additional Information
© 1981 ACM. Received August 1978; revised February 1980; accepted June 1981. This work was supported by Control Data Corporation and by the Department of Energy (Office of Basic Energy Sciences).Additional details
- Eprint ID
- 71317
- Resolver ID
- CaltechAUTHORS:20161020-124154374
- Control Data Corporation
- Department of Energy (DOE)
- Created
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2016-10-20Created from EPrint's datestamp field
- Updated
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2021-11-11Created from EPrint's last_modified field