A Contribution to the Feasibility of the Interval Gaussian Algorithm

A Contribution to the Feasibility of the Interval Gaussian Algorithm We apply the interval Gaussian algorithm to an n × n interval matrix [A] whose comparison matrix ⟨[A]⟩ is generalized diagonally dominant. For such matrices we prove conditions for the feasibility of this method, among them a necessary and sufficient one. Moreover, we prove an equivalence between a well-known sufficient criterion for the algorithm on H matrices and a necessary and sufficient one for interval matrices whose midpoint is the identity matrix. For the more general class of interval matrices which also contain the identity matrix, but not necessarily as midpoint, we derive a criterion of infeasibility. For general matrices [A] we show how the feasibility of reducible interval matrices is connected with that of irreducible ones. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Reliable Computing Springer Journals

A Contribution to the Feasibility of the Interval Gaussian Algorithm

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Publisher
Springer Journals
Copyright
Copyright © 2006 by Springer Science + Business Media, Inc.
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.
10.1007/s11155-006-4876-0
Publisher site
See Article on Publisher Site

Abstract

We apply the interval Gaussian algorithm to an n × n interval matrix [A] whose comparison matrix ⟨[A]⟩ is generalized diagonally dominant. For such matrices we prove conditions for the feasibility of this method, among them a necessary and sufficient one. Moreover, we prove an equivalence between a well-known sufficient criterion for the algorithm on H matrices and a necessary and sufficient one for interval matrices whose midpoint is the identity matrix. For the more general class of interval matrices which also contain the identity matrix, but not necessarily as midpoint, we derive a criterion of infeasibility. For general matrices [A] we show how the feasibility of reducible interval matrices is connected with that of irreducible ones.

Journal

Reliable ComputingSpringer Journals

Published: Jan 1, 2006

References

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