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An Interval Algorithm for Bounding the Ranges of Real-Valued Functions of One Real Variable

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Reliable Computing

Abstract

An interval algorithm FRANGE which determines computationally rigorous bounds on the ranges of functions f : R1 → R1 [a, b] c R1 with prescribed over-estimation is described. It is assumed that f ∈ C2(D) where D c R1 is an open interval containing [a, b]. The algorithm FRANGE is based on an algorithm due to Rall and offers a choice of four selections of function, derivative and slope evaluations. Numerical results from a Fortran 90 implementation of FRANGE are presented.

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Authors and Affiliations

  1. University of St Andrews, School of Mathematical and Computational Sciences, Mathematical Institute, North Haugh, St Andrews, Fife, KY16 9SS, Scotland

    Michael A. Wolfe

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  1. Michael A. Wolfe
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Wolfe, M.A. An Interval Algorithm for Bounding the Ranges of Real-Valued Functions of One Real Variable. Reliable Computing 3, 31–50 (1997). https://doi.org/10.1023/A:1009973905665

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