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BIT Numerical Mathematics

, Volume 16, Issue 3, pp 338–339 | Cite as

A short note on convergence near a high order zero

  • Gaston H. Gonnet
Scientific Notes

Abstract

The behaviour of different iteration schemes, when used to find a high order zero, is studied from the point of view of function value reduction. It is found that the ratio between successive function values, for a given scheme, converges to a value for increasing order of the zero.

Keywords

Computational Mathematic Order Zero Short Note Iteration Scheme Successive Function 
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.

References

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    ALTRAN Programmers guide, Bell Labs., Murray Hill, N.J.Google Scholar
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    R. B. Brent,An algorithm with guaranteed convergence for finding a zero of a function, Computer Journal, Vol. 14–4 (Apr. 1971). pp. 422–425.CrossRefGoogle Scholar
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    J. C. P. Bus and T. J. Dekker,Two efficient algorithms with guaranteed convergence for finding a zero of a function, TOMS Vol. 1–4 (Dec. 1975). pp. 330–345.CrossRefGoogle Scholar
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    G. W. Stewart,Convergence of Multipoint Iterations to Multiple Zeros, SIAM J.N.A. Vol. 11–16 (1974) pp. 1105–1120.CrossRefGoogle Scholar
  5. 5.
    D. Woodhouse,A note on the Secant Method, BIT Vol. 15–3 (1975), pp. 323–327.CrossRefGoogle Scholar

Copyright information

© BIT Foundations 1976

Authors and Affiliations

  • Gaston H. Gonnet
    • 1
  1. 1.Department of cs MathematicsUniversity of WaterlooWaterlooCanada

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