Some results on convergence acceleration for the E-algorithm
Fdil, A.
Applicationes Mathematicae, Tome 24 (1997), p. 393-413 / Harvested from The Polish Digital Mathematics Library
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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

Publié le : 1997-01-01
EUDML-ID : urn:eudml:doc:219180 
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     title = {Some results on convergence acceleration for the E-algorithm},
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     volume = {24},
     year = {1997},
     pages = {393-413},
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Fdil, A. Some results on convergence acceleration for the E-algorithm. Applicationes Mathematicae, Tome 24 (1997) pp. 393-413. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-zmv24i4p393bwm/

[000] [1] C. Brezinski, Algorithmes d'Accélération de la Convergence. Etude Numérique, Technip, Paris, 1978. | Zbl 0396.65001

[001] [2] C. Brezinski, A general extrapolation algorithm, Numer. Math. 35 (1980), 175-187. | Zbl 0444.65001

[002] [3] C. Brezinski and M. Redivo Zaglia, Extrapolation Methods, Theory and Practice, North-Holland, Amsterdam, 1991. | Zbl 0814.65001

[003] [4] W. F. Ford and D. A. Smith, Acceleration of linear and logarithmic convergence, SIAM J. Numer. Anal. 16 (1979), 223-240. | Zbl 0407.65002

[004] [5] L. Fox, Romberg integration for a class of singular integrands, Comput. J. 10 (1967), 87-93. | Zbl 0158.16001

[005] [6] T. Håvie, Error derivation in Romberg integration, BIT 12 (1972), 516-527. | Zbl 0268.65019

[006] [7] T. Håvie, Generalized Neville type extrapolation schemes, ibid. 19 (1979), 204-213. | Zbl 0404.65001

[007] [8] D. C. Joyce, Survey of extrapolation processes in numerical analysis, SIAM Rev. 13 (1972), 435-487. | Zbl 0229.65005

[008] [9] D. Levin, Development of nonlinear transformations for improving convergence of sequences, Internat. J. Computer Math. 3 (1973), 371-388. | Zbl 0274.65004

[009] [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. | Zbl 0336.65015

[010] [11] J. N. Lyness and E. de Doncker-Kapenga, On quadrature error expansions, Part I, J. Comput. Appl. Math. 17 (1987), 131-149. | Zbl 0621.41021

[011] [12] J. N. Lyness and B. W. Ninham, Numerical quadrature and asymptotic expansions, Math. Comput. 21 (1967), 162-178. | Zbl 0178.18402

[012] [13] D. Shanks, Non-linear transformations of divergent and slowly convergent sequences, J. Math. Phys. 34 (1955), 1-42. | Zbl 0067.28602

[013] [14] J. Wimp, Sequence Transformations and their Applications, Academic Press, New York, 1984. | Zbl 0566.47018