A Limitation for Underestimation Via Twin Arithmetic

A Limitation for Underestimation Via Twin Arithmetic Computing an enclosure for the range of a rational function over an interval is one of the main goals of interval analysis. One way to obtain such an enclosure is to use interval arithmetic evaluation of a formula for the function. Often one would like to check how close the overestimation is to the correct range. Kreinovich, Nesterov, and Zheludeva (Reliable Computing 2(2) (1996)) suggested a new kind of twin arithmetic which produces a twin of intervals at the same time: the usual enclosure, i.e., an interval which is an overestimation for the range, and an interval which is contained in the range, i.e. an interval which is an underestimation for the range. We show in this paper that in certain cases the computed inner interval is much smaller than the correct range. For example, if the function has the same value in the two endpoints of the interval then the inner interval is either empty or contains only one point. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Reliable Computing Springer Journals

A Limitation for Underestimation Via Twin Arithmetic

14 pages

Loading next page...

/lp/springer-journals/a-limitation-for-underestimation-via-twin-arithmetic-davVrFf8a1
Publisher site
See Article on Publisher Site

Abstract

Computing an enclosure for the range of a rational function over an interval is one of the main goals of interval analysis. One way to obtain such an enclosure is to use interval arithmetic evaluation of a formula for the function. Often one would like to check how close the overestimation is to the correct range. Kreinovich, Nesterov, and Zheludeva (Reliable Computing 2(2) (1996)) suggested a new kind of twin arithmetic which produces a twin of intervals at the same time: the usual enclosure, i.e., an interval which is an overestimation for the range, and an interval which is contained in the range, i.e. an interval which is an underestimation for the range. We show in this paper that in certain cases the computed inner interval is much smaller than the correct range. For example, if the function has the same value in the two endpoints of the interval then the inner interval is either empty or contains only one point.

Journal

Reliable ComputingSpringer Journals

Published: Oct 3, 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.

Enjoy affordable access to
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
Google Scholar,
PubMed

Create folders to
organize your research

Export folders, citations

Read DeepDyve articles

Abstract access only

Unlimited access to over
18 million full-text articles

Print

20 pages / month

PDF Discount

20% off