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On the convergence of an iterative method for bounding the inverses of an interval matrix

Über die Konvergenz eines Iterationsverfahrens zur Einschließung der Inversen einer Intervallmatrix

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Abstract

An iterative method for improving an initial inclusion for the inverses of an interval matrix is [roposed. For this we prove a convergence theorem with sufficient conditions on the width of the interval matrix in question and of the initial inclusion so that our method yields an improvement. Numerical examples are discussed.

Zusammenfassung

Ein Iterationsverfahren zur Verbesserung einer Ausgangseinschließung für die Inversen einer Intervallmatrix wird vorgeschlagen. Für dieses wird eine Konvergenzaussage bewiesen mit hinreichenden Bedingungen an die Durchmesser der fraglichen Intervallmatrix und der Ausgangseinschließung, so daß das Verfahren eine Verbesserung bringt. Numerische Beispiele werden besprochen.

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References

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  1. Fachbereich Mathematik, Universität Oldenburg, D-2900, Oldenburg, Federal Republic of Germany

    J. Herzberger

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  1. J. Herzberger
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Herzberger, J. On the convergence of an iterative method for bounding the inverses of an interval matrix. Computing 41, 153–162 (1989). https://doi.org/10.1007/BF02238739

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  • DOI: https://doi.org/10.1007/BF02238739

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