Interval Mathematical Library Based on Chebyshev and Taylor Series Expansion

In this paper, we present a mathematical library designed for use in interval solvers of nonlinear systems of equations. The library computes the validated upper and lower bounds of ranges of values of elementary mathematical functions on an interval, which are optimal in most cases. Computation of elementary functions is based on their expansion in Chebyshev and Taylor series and uses the rounded directions setting mechanism. Some original techniques developed by the authors are applied in order to provide high speed and accuracy of the computation.