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

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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

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