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

Loading next page...
 
/lp/springer_journal/on-the-applicability-of-the-interval-gaussian-algorithm-r0wgiiF5Fe
Publisher
Kluwer Academic Publishers
Copyright
Copyright © 1998 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:1009997411503
Publisher site
See Article on Publisher Site

Abstract

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.

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 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.

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