Some results on convergence acceleration for the E-algorithm

A. Fdil

Applicationes Mathematicae (1997)

  • Volume: 24, Issue: 4, page 393-413
  • ISSN: 1233-7234

Abstract

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Some new results on convergence acceleration for the E-algorithm which is a general extrapolation method are obtained. A technique for avoiding numerical instability is proposed. Some applications are given. Theoretical results are illustrated by numerical experiments

How to cite

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Fdil, A.. "Some results on convergence acceleration for the E-algorithm." Applicationes Mathematicae 24.4 (1997): 393-413. <http://eudml.org/doc/219180>.

@article{Fdil1997,
abstract = {Some new results on convergence acceleration for the E-algorithm which is a general extrapolation method are obtained. A technique for avoiding numerical instability is proposed. Some applications are given. Theoretical results are illustrated by numerical experiments},
author = {Fdil, A.},
journal = {Applicationes Mathematicae},
keywords = {extrapolation; summation of series; convergence acceleration; numerical quadrature; -algorithm; recursive algorithm},
language = {eng},
number = {4},
pages = {393-413},
title = {Some results on convergence acceleration for the E-algorithm},
url = {http://eudml.org/doc/219180},
volume = {24},
year = {1997},
}

TY - JOUR
AU - Fdil, A.
TI - Some results on convergence acceleration for the E-algorithm
JO - Applicationes Mathematicae
PY - 1997
VL - 24
IS - 4
SP - 393
EP - 413
AB - Some new results on convergence acceleration for the E-algorithm which is a general extrapolation method are obtained. A technique for avoiding numerical instability is proposed. Some applications are given. Theoretical results are illustrated by numerical experiments
LA - eng
KW - extrapolation; summation of series; convergence acceleration; numerical quadrature; -algorithm; recursive algorithm
UR - http://eudml.org/doc/219180
ER -

References

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  1. [1] C. Brezinski, Algorithmes d'Accélération de la Convergence. Etude Numérique, Technip, Paris, 1978. Zbl0396.65001
  2. [2] C. Brezinski, A general extrapolation algorithm, Numer. Math. 35 (1980), 175-187. Zbl0444.65001
  3. [3] C. Brezinski and M. Redivo Zaglia, Extrapolation Methods, Theory and Practice, North-Holland, Amsterdam, 1991. Zbl0814.65001
  4. [4] W. F. Ford and D. A. Smith, Acceleration of linear and logarithmic convergence, SIAM J. Numer. Anal. 16 (1979), 223-240. Zbl0407.65002
  5. [5] L. Fox, Romberg integration for a class of singular integrands, Comput. J. 10 (1967), 87-93. Zbl0158.16001
  6. [6] T. Håvie, Error derivation in Romberg integration, BIT 12 (1972), 516-527. Zbl0268.65019
  7. [7] T. Håvie, Generalized Neville type extrapolation schemes, ibid. 19 (1979), 204-213. Zbl0404.65001
  8. [8] D. C. Joyce, Survey of extrapolation processes in numerical analysis, SIAM Rev. 13 (1972), 435-487. Zbl0229.65005
  9. [9] D. Levin, Development of nonlinear transformations for improving convergence of sequences, Internat. J. Computer Math. 3 (1973), 371-388. Zbl0274.65004
  10. [10] J. N. Lyness, Applications of extrapolation techniques to multidimensional quadrature of some integrand functions with a singularity, J. Comput. Phys. 20 (1976), 346-364. Zbl0336.65015
  11. [11] J. N. Lyness and E. de Doncker-Kapenga, On quadrature error expansions, Part I, J. Comput. Appl. Math. 17 (1987), 131-149. Zbl0621.41021
  12. [12] J. N. Lyness and B. W. Ninham, Numerical quadrature and asymptotic expansions, Math. Comput. 21 (1967), 162-178. Zbl0178.18402
  13. [13] D. Shanks, Non-linear transformations of divergent and slowly convergent sequences, J. Math. Phys. 34 (1955), 1-42. Zbl0067.28602
  14. [14] J. Wimp, Sequence Transformations and their Applications, Academic Press, New York, 1984. Zbl0566.47018

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