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Reliable Computing

, Volume 12, Issue 2, pp 79–98 | Cite as

A Contribution to the Feasibility of the Interval Gaussian Algorithm

  • Günter Mayer
Article

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.

Keywords

Mathematical Modeling Computational Mathematic Identity Matrix Industrial Mathematic General Class 
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© Springer Science + Business Media, Inc. 2006

Authors and Affiliations

  1. 1.Institut für MathematikUniversität RostockRostockGermany

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