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Über Einige Funktionaldifferentialgleichungen Aus Der Analyse Von Algorithmen

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Zahlentheoretische Analysis II

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1262))

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Abstract

In the analysis of algorithms the study of moment generating functions often leads to functional differential equations. In this paper a number of different cases are treated in a unique framework which allows to establish explicit formulae as well as the asymptotic behaviour of the (factorial) moments.

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Literatur

  1. DE BRUIJN N.G., Asymptotic methods in analysis, Dover, New York 1981.

    MATH  Google Scholar 

  2. DOBERKAT E.E., Asymptotic estimates for the higher moments of the expected behaviour of straight insertion sort, Informat. Process.Letters 14 (1982), 179–182.

    Article  MathSciNet  MATH  Google Scholar 

  3. FELLER W., An Introduction to Probability Theory, Vol. II, Wiley, New York 1971.

    MATH  Google Scholar 

  4. GREENE D.H. und D.E. KNUTH, Mathematics for the analysis of algorithms, Birkhäuser, Boston 1982.

    MATH  Google Scholar 

  5. KEMP R., Fundamentals of the average case analysis of particular algorithms, Wiley-Teubner, Stuttgart 1984.

    Book  MATH  Google Scholar 

  6. KIRSCHENHOFER P., H.PRODINGER und R.F.TICHY, A contribution to the analysis of in situ permutation, preprint, TU Wien (1985).

    Google Scholar 

  7. KNUTH D.E., The art of computer programming, Vol. I, Addison Wesley 1969.

    Google Scholar 

  8. KNUTH D.E., The art of computer programming, Vol. III, Addison Wesley 1973.

    Google Scholar 

  9. KNUTH D.E., Mathematical analysis of algorithms, in: Information Processing 71, 19–27, North Holland 1972.

    Google Scholar 

  10. MAC LEOD L.D.G., An algorithm for in-situ permutation, Austral. Comput.J.2 (1970), 16–19.

    Google Scholar 

  11. PANNY W., A note on the higher moments of the expected behaviour of straight insertion sort, Inform.Process.Letters 22(1986), 175–178.

    Article  MathSciNet  MATH  Google Scholar 

  12. PRODINGER H., Eine Bemerkung zum asymptotischen Verhalten der höheren Momente der Anzahl der Inversionen, Anz. Österr.Akad. Wiss.Math.Nat.Kl.121(1984), 141–143.

    MathSciNet  Google Scholar 

  13. SEDGEWICK R., Mathematical Analysis of Combinatorial Algorithms, in: Probability Theory and Computer Science (G. Louchard, G. Latouche eds.), 123–206, Academic Press, London 1983.

    Google Scholar 

  14. ZAVE D.A., A series expansion involving the harmonic numbers, Inform.Process.Letters 5(1976), 75–77.

    Article  MathSciNet  MATH  Google Scholar 

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Edmund Hlawka

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© 1987 Springer-Verlag

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Kirschenhofer, P., Prodinger, H., Tichy, R.F. (1987). Über Einige Funktionaldifferentialgleichungen Aus Der Analyse Von Algorithmen. In: Hlawka, E. (eds) Zahlentheoretische Analysis II. Lecture Notes in Mathematics, vol 1262. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0078600

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  • DOI: https://doi.org/10.1007/BFb0078600

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-18015-9

  • Online ISBN: 978-3-540-47256-8

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