Skip to Main Content

Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Some new convergence acceleration methods
HTML articles powered by AMS MathViewer

by Claude Brezinski PDF
Math. Comp. 39 (1982), 133-145 Request permission

Abstract:

The E-algorithm is a general extrapolation method which includes most of the sequence transformations actually known. Some new convergence acceleration methods are derived from the E-algorithm by applying the so-called $\theta$-procedure. The algorithms thus obtained are studied. Some theoretical results are proved and numerical examples are given.
References
    A. C. Aitken, "On Bernoulli’s numerical solution of algebraic equations," Proc. Roy. Soc. Edinburgh, v. 46, 1926, pp. 289-305.
  • Claude Brezinski, Accélération de suites à convergence logarithmique, C. R. Acad. Sci. Paris Sér. A-B 273 (1971), A727–A730 (French). MR 305544
  • Claude Brezinski, Accélération de la convergence en analyse numérique, Lecture Notes in Mathematics, Vol. 584, Springer-Verlag, Berlin-New York, 1977 (French). MR 0455266
  • Claude Brezinski, Algorithmes d’accélération de la convergence, Collection Langages et Algorithmes de l’Informatique, Éditions Technip, Paris, 1978 (French). Étude numérique. MR 511657
  • C. Brezinski, A general extrapolation algorithm, Numer. Math. 35 (1980), no. 2, 175–187. MR 585245, DOI 10.1007/BF01396314
  • Florent Cordellier, Caractérisation des suites que la première étape du $\theta$-algorithme transforme en suites constantes, C. R. Acad. Sci. Paris Sér. A-B 284 (1977), no. 6, A389–A392. MR 433796
  • F. Cordellier, Sur la régularité des procédés $\delta ^{2}$ d’Aitken et $W$ de Lubkin, Padé approximation and its applications (Proc. Conf., Univ. Antwerp, Antwerp, 1979) Lecture Notes in Math., vol. 765, Springer, Berlin, 1979, pp. 20–35 (French). MR 561443
  • F. Cordellier, Analyse Numérique des Transformations de Suites et de Séries, Thesis, University of Lille. (To appear.)
  • Jean-Paul Delahaye, Liens entre la suite du rapport des erreurs et celle du rapport des différences, C. R. Acad. Sci. Paris Sér. A-B 290 (1980), no. 7, A343–A346 (French, with English summary). MR 567764
  • J.-P. Delahaye and B. Germain-Bonne, Résultats négatifs en accélération de la convergence, Numer. Math. 35 (1980), no. 4, 443–457 (French, with English summary). MR 593838, DOI 10.1007/BF01399010
  • C. Espinoza, Application de l’$\varepsilon$-Algorithme à des Suites Non Scalaires et Comparaison de quelques Résultats Numériques Obtenus avec les $\varepsilon ,\rho$ et $\theta$-Algorithmes, Mémoire de DEA, University of Lille, 1974. (Unpublished manuscript.) B. Germain-Bonne, Estimation de la Limite des Suites et Formalisation de Procédés d’Accélération de Convergence, Thesis, University of Lille, 1978.
  • T. Hȧvie, Generalized Neville type extrapolation schemes, BIT 19 (1979), no. 2, 204–213. MR 537780, DOI 10.1007/BF01930850
  • David Levin, Development of non-linear transformations of improving convergence of sequences, Internat. J. Comput. Math. 3 (1973), 371–388. MR 359261, DOI 10.1080/00207167308803075
  • Daniel Shanks, Non-linear transformations of divergent and slowly convergent sequences, J. Math. and Phys. 34 (1955), 1–42. MR 68901, DOI 10.1002/sapm19553411
  • David A. Smith and William F. Ford, Acceleration of linear and logarithmic convergence, SIAM J. Numer. Anal. 16 (1979), no. 2, 223–240. MR 526486, DOI 10.1137/0716017
  • P. Wynn, On a device for computing the $e_m(S_n)$ tranformation, Math. Tables Aids Comput. 10 (1956), 91–96. MR 84056, DOI 10.1090/S0025-5718-1956-0084056-6
  • P. Wynn, Hierarchies of arrays and function sequences associated with the epsilon algorithm and its first confluent form, Rend. Mat. (6) 5 (1972), 819–852. MR 355405
Similar Articles
  • Retrieve articles in Mathematics of Computation with MSC: 65B05
  • Retrieve articles in all journals with MSC: 65B05
Additional Information
  • © Copyright 1982 American Mathematical Society
  • Journal: Math. Comp. 39 (1982), 133-145
  • MSC: Primary 65B05
  • DOI: https://doi.org/10.1090/S0025-5718-1982-0658218-6
  • MathSciNet review: 658218