Numerical Algorithms

, Volume 10, Issue 2, pp 261–287 | Cite as

Using Markov's interval arithmetic to evaluate Bessel-Ricatti functions

  • M. C. Bartholomew-Biggs
  • S. Zakovic


This paper deals with the application of interval arithmetic to Bessel-Ricatti functions. The extended interval arithmetic we have used is due to Markov and involves a check on monotonicity of functions in an attempt to try and get sharper bounds on computed intervals. The results we obtain are compared with those from Hansen's methods (based on bounding the Taylor series remainder) and those from Moore's technique of subdividing intervals. Two techniques are considered for evaluating derivatives of functions — one uses hand-coded derivatives and the other uses automatic differentiation. Numerical results are given, using Fortran 90 implementations of interval and automatic differentiation arithmetic.


Taylor Series Sharp Bound Interval Arithmetic Automatic Differentiation Compute Interval 
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Copyright information

© J. C. Baltzer AG, Science Publishers 1995

Authors and Affiliations

  • M. C. Bartholomew-Biggs
    • 1
  • S. Zakovic
    • 1
  1. 1.Numerical Optimization CentreUniversity of HertfordshireHatfieldEngland

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