1DRANGE is a branch-and-bound algorithm for computing rigorous outer and inner bounds for the range of univariate functions, using boundary-value forms; see Chapter 2.3 (p. 60) of
- Neumaier, Interval Methods for Systems of Equations Cambridge Univ. Press, Cambridge 1990
The implementation is based on the INTLAB interval toolbox for Matlab5.
Note that this toolbox is designed for matrix computations and is very slow for univariate functions. The program should therefore be regarded as a piece of didactical software rather than of quality software. (I'd appreciate if someone provided a faster Fortran 90 or C++ implementation for the public domain.)