# 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

Reliable Computing, Volume 3 (4) – Oct 14, 2004
9 pages

/lp/springer-journals/on-a-theoretical-justification-of-the-choice-of-epsilon-inflation-in-ht89DP5yo5
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
DOI
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

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