# Sharpness in Interval Computations

Sharpness in Interval Computations Let f(x) be a rational function and let F(X) be an interval extension of f(x). When we evaluate F(X) using interval arithmetic, we obtain an interval which bounds the range of f(x) for all x in the interval X. In some cases, the lower or upper bound (or both) may be sharp. We show that we can determine whether an endpoint is sharp or not merely by keeping track of which endpoints of X are used in each step of the evaluation of F(X). We show that in certain cases, this procedure can prove that f(x) is monotonic in the interval X. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Reliable Computing Springer Journals

# Sharpness in Interval Computations

Reliable Computing, Volume 3 (1) – Oct 22, 2004
13 pages

/lp/springer_journal/sharpness-in-interval-computations-YeX8k0L95r
Publisher
Springer Journals
Subject
Mathematics; Numeric Computing; Approximations and Expansions; Computational Mathematics and Numerical Analysis; Mathematical Modeling and Industrial Mathematics
ISSN
1385-3139
eISSN
1573-1340
D.O.I.
10.1023/A:1009917818868
Publisher site
See Article on Publisher Site

### Abstract

Let f(x) be a rational function and let F(X) be an interval extension of f(x). When we evaluate F(X) using interval arithmetic, we obtain an interval which bounds the range of f(x) for all x in the interval X. In some cases, the lower or upper bound (or both) may be sharp. We show that we can determine whether an endpoint is sharp or not merely by keeping track of which endpoints of X are used in each step of the evaluation of F(X). We show that in certain cases, this procedure can prove that f(x) is monotonic in the interval X.

### Journal

Reliable ComputingSpringer Journals

Published: Oct 22, 2004

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