Convergence acceleration by the $E_{+p}$-algorithm

A. Fdil

ArticleOriginal scientific text

Title

Convergence acceleration by the $E_{+ p}$ -algorithm

Authors ¹

Affiliations

Département de Mathématiques, E.N.S. de Marrakech, B.P. S 41, 40000 Marrakech, Morocco

Abstract

A new algorithm which generalizes the E-algorithm is presented. It is called the

E_{+ p}

-algorithm. Some results on convergence acceleration for the

E_{+ p}

-algorithm are proved. Some applications are given.

Keywords

ENG

convergence acceleration, E-algorithm, linear periodic convergence, numerical quadrature

C. Brezinski, Algorithmes d'Accélération de la Convergence en Analyse Numérique. Etude numérique, Technip, Paris, 1978.
C. Brezinski, A general extrapolation algorithm, Numer. Math. 35 (1980), 175-187.
C. Brezinski and M. Redivo Zaglia, Extrapolation Methods, Theory and Practice, North-Holland, Amsterdam, 1991.
J. P. Delahaye, Sequence Transformations, Springer, Berlin, 1988.
A. Fdil, Some results on convergence acceleration for the $E$ -algorithm, Appl. Math. (Warsaw) 24 (1997), 393-413.
L. Fox, Romberg integration for a class of singular integrands, Comput. J. 10 (1967), 87-93.
H. L. Gray and W. D. Clark, On a class of nonlinear transformations and their applications to the evaluation of infinite series, J. Res. Nat. Bur. Standards Sect. B 73 (1969), 251-274.
T. Håvie, Error derivation in Romberg integration, BIT 12 (1972), 516-527.
T. Håvie, Generalized Neville type extrapolation schemes, ibid. 19 (1979), 204-213.
D. C. Joyce, Survey of extrapolation processes in numerical analysis, SIAM Rev. 13 (1971), 435-490.
J. N. Lyness, Applications of extrapolation techniques to multidimensional quadrature of some integrand functions with a singularity, J. Comput. Phys. 20 (1976), 346-364.
J. N. Lyness and B. W. Ninham, Numerical quadrature and asymptotic expansions, Math. Comp. 21 (1967), 162-177.
C. Schneider, Vereinfachte Rekursionen zur Richardson-Extrapolation in Spezialfallen, Numer. Math. 24 (1975), 177-184.
J. Wimp, Sequence Transformations and their Applications, Academic Press, New York, 1984.

Title

Convergence acceleration by the E+p-algorithm

Affiliations

Abstract

Keywords

Bibliography

Convergence acceleration by the $E_{+ p}$ -algorithm