Letter to the Editor

Letter to the Editor Reliable Computing (2006) 12: 245–246 DOI: 10.1007/s11155-006-7222-7  c Springer 2006 ˇ ´ JIRIROHN Institute of Computer Science, Czech Academy of Sciences, Pod vodar ´ enskou ve ˇzˇ´ı 2, 182 07 Prague, Czech Republic, e-mail: rohn@cs.cas.cz (Received: 25 October 2005) E. Hansen has recently published in [2] a criterion for regularity of interval matrices. As is well known, an n × n interval matrix A =[A, A]is called regular if each A ∈ A is nonsingular. Hansen first defines vertex matrices in A as matrices satisfying A ∈ {A , A } (i, j =1,…, n). (1) ij ij ij His result is then formulated as follows: An interval matrix A is regular if and only if the determinants of all the vertex matrices in A are nonzero and of the same sign. If A < A, then according to (1) for each i, j we have two options for choosing A , ij hence there are 2 mutually different vertex matrices in this case. So, in the worst case Hansen’s criterion requires evaluation of determinants of 2 matrices. This result, however, brings nothing new and is in fact much worse than a criteri- on published more than 20 http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Reliable Computing Springer Journals

Letter to the Editor

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Publisher
Kluwer Academic Publishers
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/s11155-006-7222-7
Publisher site
See Article on Publisher Site

Abstract

Reliable Computing (2006) 12: 245–246 DOI: 10.1007/s11155-006-7222-7  c Springer 2006 ˇ ´ JIRIROHN Institute of Computer Science, Czech Academy of Sciences, Pod vodar ´ enskou ve ˇzˇ´ı 2, 182 07 Prague, Czech Republic, e-mail: rohn@cs.cas.cz (Received: 25 October 2005) E. Hansen has recently published in [2] a criterion for regularity of interval matrices. As is well known, an n × n interval matrix A =[A, A]is called regular if each A ∈ A is nonsingular. Hansen first defines vertex matrices in A as matrices satisfying A ∈ {A , A } (i, j =1,…, n). (1) ij ij ij His result is then formulated as follows: An interval matrix A is regular if and only if the determinants of all the vertex matrices in A are nonzero and of the same sign. If A < A, then according to (1) for each i, j we have two options for choosing A , ij hence there are 2 mutually different vertex matrices in this case. So, in the worst case Hansen’s criterion requires evaluation of determinants of 2 matrices. This result, however, brings nothing new and is in fact much worse than a criteri- on published more than 20

Journal

Reliable ComputingSpringer Journals

Published: Jan 1, 2006

References

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