# On the Applicability of the Interval Gaussian Algorithm

On the Applicability of the Interval Gaussian Algorithm We consider a linear interval system with a regular n × n interval matrix [A] which has the form [A] = I + [-R,R]. For such a system we prove necessary and sufficient conditions for the applicability of the interval Gaussian algorithm where applicability means that the algorithm does not break down by dividing by an interval which contains zero. If this applicability is guaranteed we compare the output vector [x]G with the interval hull of the solution set $$S = \tilde x\left\{ {\left| {\exists \tilde A \in \left[ A \right]\tilde b \in \left[ b \right]} \right.:\tilde A\tilde x = \tilde b} \right\}$$ . In particular, we show that in each entry of [x]G at least one of the two bounds is optimal. Linear interval systems of the above-mentioned form arise when a given general system is preconditioned with the midpoint inverse of the underlying coefficient matrix. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Reliable Computing Springer Journals

# On the Applicability of the Interval Gaussian Algorithm

, Volume 4 (3) – Oct 14, 2004
18 pages

/lp/springer_journal/on-the-applicability-of-the-interval-gaussian-algorithm-r0wgiiF5Fe
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:1009997411503
Publisher site
See Article on Publisher Site

## 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
that matters to you.

over 12 million articles from more than
10,000 peer-reviewed journals.

All for just $49/month ### Explore the DeepDyve Library ### Unlimited reading Read as many articles as you need. Full articles with original layout, charts and figures. Read online, from anywhere. ### Stay up to date Keep up with your field with Personalized Recommendations and Follow Journals to get automatic updates. ### Organize your research It’s easy to organize your research with our built-in tools. ### 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. ### Monthly Plan • Read unlimited articles • Personalized recommendations • No expiration • Print 20 pages per month • 20% off on PDF purchases • Organize your research • Get updates on your journals and topic searches$49/month

14-day Free Trial

Best Deal — 39% off

### Annual Plan

• All the features of the Professional Plan, but for 39% off!
• Billed annually
• No expiration
• For the normal price of 10 articles elsewhere, you get one full year of unlimited access to articles.

$588$360/year

billed annually

14-day Free Trial