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Interval bounds for square roots and cube roots

Intervall-Schranken für die Quadrat- und die Kubikwurzel

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Abstract

The smallest machine representable interval containing the square root of a given machine representable number is sought. Assuming binary computers with optimal upward directed rounding, it is shown bya priori methods of error analysis that this interval may be obtained via Newton's method without using interval arithmetic. Less sharp but still useful results are obtained for the cube root.

Zusammenfassung

Gesucht ist das kleinste Maschinenzahlenintervall, das die Quadratwurzel einer gegebenen Maschinenzahl enthält. Betrachtet werden Dualmaschinen mit optimaler Rundung nach oben. Mit Hilfe vona priori Fehlerabschätzungen wird gezeigt, daß sich das gesuchte Intervall mit dem Newton-Verfahren ohne jede Intervall-Rechnung bestimmen läßt. Für die Kubikwurzel gelten weniger scharfe, aber trotzdem recht brauchbare Resultate.

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Authors and Affiliations

  1. Mathematics Research Center, University of Wisconsin, 610 Walnut Street, 53706, Madison, WI, U. S. A.

    J. M. Yohe

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  1. J. M. Yohe
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Additional information

Sponsored by the United States Army under Contract No.: DA-31-124-ARO-D-462.

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Yohe, J.M. Interval bounds for square roots and cube roots. Computing 11, 51–57 (1973). https://doi.org/10.1007/BF02239472

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  • DOI: https://doi.org/10.1007/BF02239472

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