# An Interval Algorithm for Bounding the Ranges of Real-Valued Functions of One Real Variable

An Interval Algorithm for Bounding the Ranges of Real-Valued Functions of One Real Variable An interval algorithm FRANGE which determines computationally rigorous bounds on the ranges of functions f : R1 → R1 [a, b] c R1 with prescribed over-estimation is described. It is assumed that f ∈ C2(D) where D c R1 is an open interval containing [a, b]. The algorithm FRANGE is based on an algorithm due to Rall and offers a choice of four selections of function, derivative and slope evaluations. Numerical results from a Fortran 90 implementation of FRANGE are presented. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Reliable Computing Springer Journals

# An Interval Algorithm for Bounding the Ranges of Real-Valued Functions of One Real Variable

, Volume 3 (1) – Oct 22, 2004
20 pages

/lp/springer_journal/an-interval-algorithm-for-bounding-the-ranges-of-real-valued-functions-v6rVsZZh9D
Publisher
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:1009973905665
Publisher site
See Article on Publisher Site

### Abstract

An interval algorithm FRANGE which determines computationally rigorous bounds on the ranges of functions f : R1 → R1 [a, b] c R1 with prescribed over-estimation is described. It is assumed that f ∈ C2(D) where D c R1 is an open interval containing [a, b]. The algorithm FRANGE is based on an algorithm due to Rall and offers a choice of four selections of function, derivative and slope evaluations. Numerical results from a Fortran 90 implementation of FRANGE are presented.

### Journal

Reliable ComputingSpringer Journals

Published: Oct 22, 2004

## You’re reading a free preview. Subscribe to read the entire article.

### DeepDyve is your personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

over 18 million articles from more than
15,000 peer-reviewed journals.

All for just \$49/month

### Search

Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly

### Organize

Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.

### Access

Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.

### Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

DeepDyve

DeepDyve

### Pro

Price

FREE

\$49/month
\$360/year

Save searches from
PubMed

Create lists to

Export lists, citations