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An axiomatic approach to rounded computations

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Abstract

The present paper is intended to give an axiomatic approach to rounded computations. A rounding is defined as a monotone mapping of an ordered set into a subset, which in general is called a lower respectively an upper screen. The first chapter deals with roundings in ordered sets. In the second chapter further properties of roundings in linearly ordered sets are studied. The third chapter deals with the two most important applications, the approximation of the real arithmetic on a finite screen and the approximation of the real interval arithmetic on an upper screen. Beyond these examples various further applications are possible.

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References

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Authors and Affiliations

  1. Mathematics Research Center, The University of Wisconsin, 53706, Madison, Wisconsin, USA

    U. Kulisch

  2. Institut für Angewandte Mathematik, Universität Karlsruhe, Englerstraße 2, BRD-7500, Karlsruhe, Deutschland

    U. Kulisch

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  1. U. Kulisch
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Sponsored by the Mathematics Research Center, Madison, Wisconsin, under Contract No.: DA-31-124-ARO-D-462.

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Kulisch, U. An axiomatic approach to rounded computations. Numer. Math. 18, 1–17 (1971). https://doi.org/10.1007/BF01398455

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  • DOI: https://doi.org/10.1007/BF01398455

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