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Representation of interval operations by coordinates

Koordinatenweise Durchführung der Intervalloperationen

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Abstract

We discuss possibilities of introducing coordinates for interval arithmetic so that the interval operations can be performed seperately for each coordinate. It is known that such representations exist for addition and also for multiplication. Now it is shown that there does not exist a joint representation for addition and multiplication.

Zusammenfassung

Es werden Möglichkeiten diskutiert, Koordinatendarstellungen für die Intervallarithmetik so einzuführen, daß die Intervallverknüpfungen komponentenweise ausgeführt werden können. Es ist bekannt, daß derartige Darstellungen für die Addition und auch für die Multiplikation vorhanden sind. Es wird nun gezeigt, daß es keine gemeinsame Darstellung für Addition und Multiplikation gibt.

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References

  1. Grätzer, G.: Universal algebra, p. 122. Princeton, N. J.: Van Nostrand 1968.

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  2. Ratschek, H.: Teilbarkeitskriterien der Intervallarithmetik. J. Reine Angew. Math.252, 128–138 (1972).

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  3. Ratschek, H.: Die subdirekte Unzerlegbarkeit der Intervallrechnung. J. Reine Angew. Math.299/300, 287–293 (1978).

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Authors and Affiliations

  1. Mathematisches Institut, Universität Düsseldorf, Universitätsstrasse 1, D-4000, Düsseldorf, Federal Republic of Germany

    H. Ratschek

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  1. H. Ratschek
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Additional information

Short version of a paper presented at the meeting “Fundamentals of Numerical Computation”, Berlin, June 5 to 8, 1979.

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Ratschek, H. Representation of interval operations by coordinates. Computing 24, 93–96 (1980). https://doi.org/10.1007/BF02281714

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  • DOI: https://doi.org/10.1007/BF02281714

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