ACETAF: A software package for computing validated bounds for Taylor coefficients of analytic functions

ABSTRACT

This article presents methods for practical computation of verified bounds for Taylor coefficients of analytic functions. These bounds are constructed from Cauchy's estimate and from some of its modifications. Interval arithmetic is used to obtain rigorous results.

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INDEX TERMS

Primary Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.0 General
          Subjects: Interval arithmetic

Additional Classification:
  G. Mathematics of Computing
  G.4 MATHEMATICAL SOFTWARE
      Subjects: Algorithm design and analysis

General Terms:
Algorithms, Reliability, Verification

Keywords:
Analytic functions, bounds for Taylor coefficients