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BIT Numerical Mathematics

, Volume 3, Issue 3, pp 175–195 | Cite as

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.

Keywords

Computational Mathematic Algorithmic Formula ALGOL Programme Singular Rule 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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