Abstract
TheE-algorithm is the most general extrapolation algorithm actually known. The aim of this paper is to provide a new approach to this algorithm. This approach gives a deeper insight into theE-algorithm, and allows one to obtain new properties and to relate it to other algorithms. Some extensions of the procedure are discussed.
Similar content being viewed by others
References
B. Beckermann, A connection between theE-algorithm and the epsilon-algorithm, in:Numerical and Applied Mathematics, ed. C. Brezinski (Baltzer, Basel, 1989) pp. 443–446.
C. Brezinski, A general extrapolation algorithm, Numer. Math. 35(1980)175–187.
C. Brezinski, The Mühlbach-Neville-Aitken algorithm and some extensions, BIT 20(1980) 444–451.
C. Brezinski, A survey of iterative extrapolation by theE-algorithm, Det Kong. Norske Vid. Selsk. skr. 2(1989)1–26.
C. Brezinski, Algebraic properties of theE-transformation, in:Numerical Analysis and Mathematical Modelling, Banach Center Publications, Vol. 24 (PWN, Warsaw, 1990) pp. 85–90.
C. Brezinski and A.C. Matos, A derivation of extrapolation algorithms based on error estimates, J. Comput. Appl. Math., to appear.
C. Brezinski and M. Redivo-Zaglia,Extrapolation Methods. Theory and Practice (North-Holland, Amsterdam, 1991).
C. Brezinski and A. Salam, Matrix and vector sequence transformations revisited, submitted.
C. Brezinski and G. Walz, Sequences of transformations and triangular recursion schemes with applications in numerical analysis, J. Comput. Appl. Math. 34(1991)361–383.
C. Carstensen, On a general epsilon algorithm, in:Numerical and Applied Mathematics, ed. C. Brezinski (Baltzer, Basel, 1989) pp. 437–441.
W.F. Ford and A. Sidi, An algorithm for a generalization of the Richardson extrapolation process, SIAM J. Numer. Anal. 24(1987)1212–1232.
T. Håvie, Generalized Neville type extrapolation schemes, BIT 19(1979)204–213.
A.C. Matos and M. Prévost, Acceleration property of theE-algorithm, Numer. Algor. 2(1992) 393–408.
G. Meinardus and G.D. Taylor, Lower estimates for the error of best uniform approximation, J. Approx. Theory 16(1976)150–161.
G. Mühlbach, A recurrence formula for generalized divided differences and some applications, J. Approx. Theory 9(1973)165–172.
G. Mühlbach, Newton- und Hermite-Interpolation mit Čebyšev-Systemen, Z. Angew. Math. Mech. 54(1974)541–550.
G. Mühlbach, Neville-Aitken algorithms for interpolation by functions of Čebyšev-systems in the sense of Newton and in a generalized sense of Hermite, in:Theory of Approximation, with Applications, ed. A.G. Law and B.N. Sahney(Academic Press, New York, 1967) pp. 200–212.
G. Mühlbach, The general Neville-Aitken algorithm and some applications, Numer. Math. 31(1978)97–110.
G. Mühlbach, The general recurrence relation for divided differences and the general Newton-interpolation-algorithm with applications to trigonometric interpolation, Numer. Math. 32(1979) 393–408.
M. Prévost, Acceleration property for theE-algorithm and an application to the summation of series, Adv. Comput. Math. 2(1994)319–341.
C. Schneider, Vereinfachte Rekursionen zur Richardson-Extrapolation in Spezialfällen, Numer. Math. 24(1975)177–184.
D. Shanks, Non linear transformations of divergent and slowly convergent sequences, J. Math. Phys. 34(1951)1–42.
A. Sidi, An algorithm for a special case of a generalization of the Richardson extrapolation process, Numer. Math. 38(1982)299–307.
A. Sidi, On a generalization of the Richardson extrapolation process, Numer. Math. 57(1990) 365–377.
E.J. Weniger, Nonlinear sequence transformations for the acceleration of convergence and the summation of divergent series, Comput. Phys. Rep. 10(1989)189–371.
P. Wynn, On a device for computing theS n) transformation, MTAC 10(1956)91–96.
P. Wynn, Confluent forms of certain nonlinear algorithms. Arch. Math. 11(1960)223–234.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Brezinski, C., Redivo-Zaglia, M. A general extrapolation procedure revisited. Adv Comput Math 2, 461–477 (1994). https://doi.org/10.1007/BF02521609
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02521609