BIT Numerical Mathematics

, Volume 31, Issue 2, pp 276–285 | Cite as

Numerical evaluation of analytic functions by Cauchy's theorem

  • N. I. Ioakimidis
  • K. E. Papadakis
  • E. A. Perdios
Part II Numerical Mathematics


The use of the Cauchy theorem (instead of the Cauchy formula) in complex analysis together with numerical integration rules is proposed for the computation of analytic functions and their derivatives inside a closed contour from boundary data for the analytic function only. This approach permits a dramatical increase of the accuracy of the numerical results for points near the contour. Several theoretical results about this method are proved. Related numerical results are also displayed. The present method together with the trapezoidal quadrature rule on a circular contour is investigated from a theoretical point of view (including error bounds and corresponding asymptotic estimates), compared with the numerically competitive Lyness-Delves method and rederived by using the Theotokoglou results on the error term. Generalizations for the present method are suggested in brief.

AMS Categories

primary: 65E05 secondary: 30E20, 65D32 

Key-words and phrases

analytic functions asymptotic estimates Cauchy formula Cauchy theorem circle contour complex contour integrals error bounds error term numerical integration Taylor series trapezoidal quadrature rule 


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Copyright information

© BIT Foundations 1991

Authors and Affiliations

  • N. I. Ioakimidis
    • 1
  • K. E. Papadakis
    • 1
  • E. A. Perdios
    • 1
  1. 1.Division of Applied Mathematics and Mechanics, School of EngineeringUniversity of PatrasPatrasGreece

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