A lower bound for range enclosure in interval arithmetic

Authors:
Affiliations:
Venue:
Theoretical Computer Science
Year:
2002

Citing 6
Cited 0

On higher order centered forms

Computing
On the approximation of the range of values by interval expressions

Computing
Enclosure methods

Computer arithmetic and self-validating numerical methods
A sufficient condition for non-overestimation in interval arithmetic

Computing
Methods and Applications of Interval Analysis (SIAM Studies in Applied and Numerical Mathematics) (Siam Studies in Applied Mathematics, 2.)

Methods and Applications of Interval Analysis (SIAM Studies in Applied and Numerical Mathematics) (Siam Studies in Applied Mathematics, 2.)
On hardware support for interval computations and for soft computing: theorems

IEEE Transactions on Fuzzy Systems

Quantified Score

Hi-index	5.23

Visualization

Abstract

Including the range of a rational function over an interval is an important problem in numerical computation. A direct interval arithmetic evaluation of a formula for the function yields in general a superset with an error linear in the width of the interval. Special formulas like the centered forms yield a better approximation with a quadratic error. Alefeld posed the question whether in general there exists a formula whose interval arithmetic evaluation gives an approximation of better than quadratic order. In this paper we show that the answer to this question is negative if in the interval arithmetic evaluation of a formula only the basic four interval operations +, -, ., / are used.