Differentiation formulas for analytic functions
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- by J. N. Lyness PDF
- Math. Comp. 22 (1968), 352-362 Request permission
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
- J. N. Lyness and C. B. Moler, Numerical differentiation of analytic functions, SIAM J. Numer. Anal. 4 (1967), 202–210. MR 214285, DOI 10.1137/0704019
- J. N. Lyness, The calculation of Fourier coefficients, SIAM J. Numer. Anal. 4 (1967), 301–314. MR 216791, DOI 10.1137/0704027 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. G. Pólya & G. Szegö, Aufgaben und Lehrsätze aus der Analysis, Vol. 2, Springer-Verlag, Berlin, 1954. MR 15, 512.
Additional Information
- © Copyright 1968 American Mathematical Society
- Journal: Math. Comp. 22 (1968), 352-362
- MSC: Primary 65.55
- DOI: https://doi.org/10.1090/S0025-5718-1968-0230468-5
- MathSciNet review: 0230468