Interval Slopes for Rational Functions and Associated Centered Forms
R. Krawczyk, Arnold Neumaier · SIAM Journal on Numerical Analysis · 1985
For an arithmetic expression $f(x)$ involving N rational operations, an $O(N)$ algorithm is given which computes an interval enclosure for the set of slopes $f[ {x,z} ]$ where x ranges over an interval X. Applications to real and complex centered forms are given, resulting in improvements over previous results by Ratschek [SIAM J. Numer. Anal., 17 (1980), pp. 656–662] and Petković [Freiburger Intervall-Berichte, 83 (2) (1983), pp. 33–50].