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A Contribution to the Feasibility of the Interval Gaussian Algorithm

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Reliable Computing

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.

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  1. Institut für Mathematik, Universität Rostock, D-18051, Rostock, Germany

    Günter Mayer

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  1. Günter Mayer
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Correspondence to Günter Mayer.

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Dedicated to Professor Dr. H. J. Stetter, Wien, on the occasion of his 75th birthday

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Mayer, G. A Contribution to the Feasibility of the Interval Gaussian Algorithm. Reliable Comput 12, 79–98 (2006). https://doi.org/10.1007/s11155-006-4876-0

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  • DOI: https://doi.org/10.1007/s11155-006-4876-0

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