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Schnelle Berechnung von Kettenbruchentwicklungen

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A. SchönhageAuthors Info & Claims

Acta Informatica, Volume 1, Issue 2

Pages 139 - 144

https://doi.org/10.1007/BF00289520

Published: 01 June 1971 Publication History

Abstract

A method, given by D. E. Knuth for the computation of the greatest common divisor of two integers u, v and of the continued fraction for u/v is modified in such a way that only O(n(lg n)²(lglg n)) elementary steps are used for u,v<.2 ⁿ.

Ein von D. E. Knuth angegebenes Verfahren, für ganze Zahlen u, v den gröβten gemeinsamen Teiler und den Kettenbruch für u/v zu berechnen, wird so modifiziert, daβ für n-stellige Zahlen nur O(n(lg n)² (lglg n)) elementare Schritte gebraucht werden.

References

[1]

Knuth, D. E.: The analysis of algorithms. Vortrag Intern. Math.-Kongreß Nizza 1970.

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[2]

Perron, O.: Die Lehre von den Kettenbrüchen. Bd. 1, 3-Aufl. 1954, Teubner.

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[3]

Schönhage, A., Straßen, V.: Schnelle Multiplikation großer Zahlen. Erscheint demnächst in Computing.

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Acta Informatica Volume 1, Issue 2

June 1971

94 pages

ISSN:0001-5903

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Springer-Verlag

Berlin, Heidelberg

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Published: 01 June 1971

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