On a Theoretical Justification of the Choice of Epsilon-Inflation in PASCAL-XSC

On a Theoretical Justification of the Choice of Epsilon-Inflation in PASCAL-XSC In many interval computation methods, if we cannot guarantee a solution within a given interval, it often makes sense to "inflate" this interval a little bit. There exist many different "inflation" methods. The authors of PASCAL-XSC, after empirically comparing the behavior of different inflation methods, decided to implement the formula [x-,x+]ε = [(1 + ε)x- - ε · x+, (1 + ε)x+ - ε · x-]. A natural question is: Is this choice really optimal (in some reasonable sense), or is it only an empirical approximation to the truly optimal choice? http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Reliable Computing Springer Journals

On a Theoretical Justification of the Choice of Epsilon-Inflation in PASCAL-XSC

Loading next page...
 
/lp/springer_journal/on-a-theoretical-justification-of-the-choice-of-epsilon-inflation-in-ht89DP5yo5
Publisher
Springer Journals
Copyright
Copyright © 1997 by Kluwer Academic Publishers
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:1009905822286
Publisher site
See Article on Publisher Site

Abstract

In many interval computation methods, if we cannot guarantee a solution within a given interval, it often makes sense to "inflate" this interval a little bit. There exist many different "inflation" methods. The authors of PASCAL-XSC, after empirically comparing the behavior of different inflation methods, decided to implement the formula [x-,x+]ε = [(1 + ε)x- - ε · x+, (1 + ε)x+ - ε · x-]. A natural question is: Is this choice really optimal (in some reasonable sense), or is it only an empirical approximation to the truly optimal choice?

Journal

Reliable ComputingSpringer Journals

Published: Oct 14, 2004

References

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

Explore the DeepDyve Library

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.

See the journals in your area

DeepDyve

Freelancer

DeepDyve

Pro

Price

FREE

$49/month
$360/year

Save searches from
Google Scholar,
PubMed

Create lists to
organize your research

Export lists, citations

Read DeepDyve articles

Abstract access only

Unlimited access to over
18 million full-text articles

Print

20 pages / month

PDF Discount

20% off