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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.

References [Enhancements On Off] (What's this?)

  • [1] J. N. Lyness & C. B. Moler, "Numerical differentiation of analytic functions," SIAM J. Numer. Anal., v. 4, 1967, pp. 202-210. MR 0214285 (35:5136)
  • [2] J. N. Lyness, "The calculation of Fourier coefficients," SIAM J. Numer. Anal., v. 4, 1967, pp. 301-315. MR 0216791 (35:7620)
  • [3] J. N. Lyness, Numerical Algorithms Based on the Theory of Complex Variables, Proc. 22nd Nat. Conf. A.C.M. Publication P-67, 1967, pp. 125-133.
  • [4] G. Pólya & G. Szegö, Aufgaben und Lehrsätze aus der Analysis, Vol. 2, Springer-Verlag, Berlin, 1954. MR 15, 512.

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Article copyright: © Copyright 1968 American Mathematical Society

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