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Miscellanea

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Part of the book series: Contemporary Mathematicians ((CM))

Abstract

Here, five “miscellaneous” papers of Walter Gautschi are commented on, [GA96, GA124, GA125, GA175, GA197], preceded by some personal reminiscences.

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Notes

  1. 1.

    With the help of Walter, we later found the Fortran implementation in [2].

  2. 2.

    Many thanks to Hui Zhang, who also implemented the algorithm independently, so we could compare.

  3. 3.

    Compilation would make this certainly much faster.

  4. 4.

    Many thanks to Ivan Graham for suggesting this useful example during a conference in Urümqi in August 2012.

  5. 5.

    square-root snail

References

  1. Philip J. Davis. Spirals: from Theodorus to chaos With contributions by Walter Gautschi and Arieh Iserles. A K Peters, Wellesley, MA, 1993. x+237 pp. ISBN: 1-56881-010-5.

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  2. Bernard N. Flury and Gregory Constantine. The F-G diagonalization algorithm. Algorithm AS 211. Applied Statistics 34:177–183, 1985

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  3. Martin J. Gander and Alan H. Karp. Stable computation of high order Gauss quadrature rules using discretization for measures in radiation transfer. J. Quantitative Spectroscopy Radiative Transfer, 68(2):213–223, 2001.

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  4. Edmund Hlawka. Gleichverteilung und Quadratwurzelschnecke. Monatsh. Math., 89(1):19–44, 1980. (Excerpted English translation in [1, pp. 157-167].)

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  5. A. Kuznetsov. Asymptotic approximations to the Hardy–Littlewood function. J. Comput. Appl. Math., 237:603–613, 2013.

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  6. Jörg Waldvogel. Analytic continuation of the Theodorus spiral. joerg.waldvogel@ sam.math.ethz.ch

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Gander, M.J. (2014). Miscellanea. In: Brezinski, C., Sameh, A. (eds) Walter Gautschi, Volume 3. Contemporary Mathematicians. Birkhäuser, New York, NY. https://doi.org/10.1007/978-1-4614-7132-5_5

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