BIT Numerical Mathematics

, Volume 3, Issue 3, pp 175–195

Singular rules for certain non-linear algorithms

Article

Abstract

Certain simple non-linear algorithms which have useful application in numerical analysis have recently been introduced. When using the formulae of these algorithms it may sometimes occur that a quantity is numerically ill-determined. As a result of this and because of the way in which the algorithmic formulae are used, all quantities lying in a certain sector become ill-determined. By considering theε-,ϱ-, andqd-algorithms in detail it is shown how this misfortune may be overcome. ALGOL programmes are developed to show how the derived formulae may be mechanized.

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References

  1. 1.
    Wynn, P.,On a Device for Computing the e m(S n)Transformation, MTAC 10, 91–96 (1956).Google Scholar
  2. 2.
    Wynn, P.,On a Procrustean Technique for the Numerical Transformation of Slowly Convergent Sequences and Series, Proc. Cambr. Phil. Soc. 52, 665–671.Google Scholar
  3. 3.
    Rutishauser, H.,Der Quotienten-Differenzen-Algorithmus, Birkhauser Verlag, Basel/Stuttgart 1957.Google Scholar
  4. 4.
    Bauer, F. L.,The g-Algorithm, J. Soc. Indust. Appl. Math., Vol. 8, No. 1, 1960, 1–17.Google Scholar

Copyright information

© BIT Foundations 1963

Authors and Affiliations

  • P. Wynn
    • 1
  1. 1.Mathematisch CentrumAmsterdam

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