Automatic selection of sequence transformations
Author:
J.-P. Delahaye
Journal:
Math. Comp. 37 (1981), 197-204
MSC:
Primary 65B99
DOI:
https://doi.org/10.1090/S0025-5718-1981-0616372-5
MathSciNet review:
616372
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: Some methods of automatic selection of sequence transformations for accelerating the convergence of sequences are presented. Two theorems show the efficiency of these methods. This is confirmed by numerical experiments.
- Claude Brezinski, Accélération de suites à convergence logarithmique, C. R. Acad. Sci. Paris Sér. A-B 273 (1971), A727–A730 (French). MR 305544
- C. Brezinski, Études sur les $\varepsilon $- et $\rho $-algorithmes, Numer. Math. 17 (1971), 153–162 (French, with English summary). MR 286242, DOI https://doi.org/10.1007/BF01406003
- 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, Éditions Technip, Paris, 1978 (French). Étude numérique; Collection Langages et Algorithmes de l’Informatique. MR 511657
- C. Brezinski, A general extrapolation algorithm, Numer. Math. 35 (1980), no. 2, 175–187. MR 585245, DOI https://doi.org/10.1007/BF01396314 F. Cordellier, Sur la Régularité des Procédés ${\delta ^2}$ d’Aitken et W de Lubkin, Publ. A. N. O. No. 10, Univ. des Sci. et Tech, de Lille, 1979. J. P. Delahaye, Etude Générale des Procédés de Choix Entre Transformations de Suites en Accélération de la Convergence, Publ. A. N. O., Univ. des Sci. et Tech. de Lille. (To appear.) P. J. Laurent, Etude des procédés d’Extrapolation en Analyse Numérique, Thèse, Grenoble, 1964.
- K. J. Overholt, Extended Aitken acceleration, Nordisk Tidskr. Informationsbehandling (BIT) 5 (1965), 122–132. MR 179907, DOI https://doi.org/10.1007/bf01939615
- Daniel Shanks, Non-linear transformations of divergent and slowly convergent sequences, J. Math. and Phys. 34 (1955), 1–42. MR 68901, DOI https://doi.org/10.1002/sapm19553411
- P. Wynn, On a device for computing the $e_m(S_n)$ tranformation, Math. Tables Aids Comput. 10 (1956), 91–96. MR 84056, DOI https://doi.org/10.1090/S0025-5718-1956-0084056-6
Retrieve articles in Mathematics of Computation with MSC: 65B99
Retrieve articles in all journals with MSC: 65B99
Additional Information
Article copyright:
© Copyright 1981
American Mathematical Society