Interval Arithmetic, Affine Arithmetic, Taylor Series Methods: Why, What Next?

Authors

Nedialko S. Nedialkov
Vladik Kreinovich, The University of Texas at El PasoFollow
Scott A. Starks, The University of Texas at El PasoFollow

Publication Date

9-2003

Comments

Technical Report: UTEP-CS-03-03b

Published in Numerical Algorithms, 2004, Vol. 37, pp. 325-336.

Abstract

In interval computations, the range of each intermediate result r is described by an interval [r]. To decrease excess interval width, we can keep some information on how r depends on the input x=(x1,...,xn). There are several successful methods of approximating this dependence; in these methods, the dependence is approximated by linear functions (affine arithmetic) or by general polynomials (Taylor series methods). Why linear functions and polynomials? What other classes can we try? These questions are answered in this paper.