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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



Differentiation formulas for analytic functions

Author: J. N. Lyness
Journal: Math. Comp. 22 (1968), 352-362
MSC: Primary 65.55
MathSciNet review: 0230468
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Abstract: In a previous paper (Lyness and Moler $[1]$), several closely related formulas of use for obtaining a derivative of an analytic function numerically are derived. Each of these formulas consists of a convergent series, each term being a sum of function evaluations in the complex plane. In this paper we introduce a simple generalization of the previous methods; we investigate the "truncation error" associated with truncating the infinite series. Finally we recommend a particular differentiation rule, not given in the previous paper.

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Article copyright: © Copyright 1968 American Mathematical Society