BIT Numerical Mathematics

, Volume 13, Issue 1, pp 8–15 | Cite as

A note on a paper by G.Pólya

  • M. R. Farmer
  • G. Loizou


This note is concerned with the computer implementation of Pólya's paper [8] for determining the zeros of a special class of entire functions. Grau's modification to the Graeffe process [6] is utilised to bound the iterated coefficients.


Computational Mathematic Entire Function Special Class Computer Implementation Iterate Coefficient 
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  1. 1.
    M. Abramowitz and I. A. Stegun (Ed.),Handbook of Mathematical Functions, National Bureau of Standards, Applied Mathematics Series 55, Washington, 1964.Google Scholar
  2. 2.
    H. Dirschmid, Zur Einschließung der Eigenwerte vollstetiger positiver Operatoren in separablen Hilbert-Räumen I, II, Computing 5 (1970), 17–26, 119–127.Google Scholar
  3. 3.
    M. R. Farmer and G. Loizou,Computation of the Zeros of a Special Class of Entire Functions, unpublished.Google Scholar
  4. 4.
    H. Gerber,First One Hundred Zeros of J 0 (x) Accurate to Nineteen Significant Figures, Math. Comp. 18 (1964), 319–322.Google Scholar
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    A. A. Grau,Modified Graeffe Method (Algorithm 256), Comm. ACM 8 (1965), 379–380.CrossRefGoogle Scholar
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    A. A. Grau,On the Reduction of Number Range in the Use of the Graeffe Process, J. ACM 10 (1963), 538–544.CrossRefGoogle Scholar
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    I. D. Hill,Procedures for the Basic Arithmetical Operations in Multiple-length Working (Algorithm 34), The Computer Journal 11 (1968), 232–235.Google Scholar
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    G. Pólya,Graeffe's Method for Eigenvalues, Num. Math. 11 (1968), 315–319.Google Scholar
  9. 9.
    A. H. Stroud and D. Secrest,Gaussian Quadrature Formulas, Prentice-Hall, Englewood Cliffs, New Jersey, 1966.Google Scholar

Copyright information

© BIT Foundations 1973

Authors and Affiliations

  • M. R. Farmer
    • 1
  • G. Loizou
    • 1
  1. 1.Department of Computer Science Birkbeck CollegeUniversity of LondonLondonEngland

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