... years. Today,it is a well established tool for the calculation of rigorous error bounds for many problemsin numerical analysis.Despite its overall success, interval arithmetic suffers from two ... functions, an interval versionof Newton’s method, a chapter on automatic differentiation, and algorithms for the validatedsolution of ODEs. Extensive introductions to interval computations have also ... meaningful.Interval arithmetic provides a tool for controlling roundoff errors automatically. Insteadof approximating x by a machine number, the real value x is enclosed into a real intervalX = [x, x] with...