PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
1996-1997 | 24 | 3 | 299-306
Tytuł artykułu

Some convergence acceleration processes for a class of vector sequences

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Let $(S_n)$ be some vector sequence, converging to S, satisfying $S_n - S \sim ϱ ^n n^{θ}(β_0 + β_1 n^{-1} + β_2 n^{-2} + ...), 0 \lt |ϱ|\lt 1 , θ \lt 0$, where $β_0(\ne 0), β_1,...$ are constant vectors independent of n. The purpose of this paper is to provide acceleration methods for these vector sequences. Comparisons are made with some known algorithms. Numerical examples are also given.
Rocznik
Tom
24
Numer
3
Strony
299-306
Opis fizyczny
Daty
wydano
1997
otrzymano
1996-03-01
Twórcy
  • Laboratoire d'Analyse Numérique et D'optimisation, Université des Sciences et Technologies de Lille, 59655 Villeneuve d'Ascq Cedex, France
Bibliografia
  • [1] A. C. Aitken, On Bernoulli's numerical solution of algebraic equations, Proc. Roy. Soc. Edinburgh 46 (1926), 289-305.
  • [2] S. Bhowmick, R. Bhattacharya and D. Roy, Iterations of convergence accelerating nonlinear transforms, Comput. Phys. Comm. 54 (1989), 31-46.
  • [3] C. Brezinski, Algorithmes d'Accélération de la Convergence, Etude Numérique, Editions Technip, Paris, 1978.
  • [4] C. Brezinski and M. Redivo Zaglia, Extrapolation Methods. Theory and Practice, Math. Stud. in Comput. Math. 2, North-Holland, 1991.
  • [5] P. R. Graves-Morris, Extrapolation method for vector sequences, Numer. Math. 61 (1992), 475-487.
  • [6] B. M. Irons and R. C. Tuck, A version of the Aitken accelerator for computer iteration, Internat. J. Numer. Methods Engrg. 1 (1969), 275-277.
  • [7] N. Osada, Extensions of Levin's transformations to vector sequences, Numer. Algorithms 2 (1992), 121-132.
  • [8] L. B. Rall, Convergence of the Newton process to multiple solutions, Numer. Math. 9 (1966), 23-37.
  • [9] G. W. Reddien, Newton's method and high order singularities, Comput. Math. Appl. 5 (1979), 79-86.
  • [10] E. J. Weniger, On the derivation of iterated sequence transformations for the acceleration of convergence and the summation of divergent series, Comput. Phys. Comm. 64 (1991), 19-45.
  • [11] J. Wimp, Sequence Transformations and their Applications, Academic Press, New York, 1981.
  • [12] P. Wynn, Acceleration techniques for iterated vector and matrix problems, Math. Comp. 16 (1962), 301-322.
  • [13] P. Wynn, Transformations de séries à l'aide de l'ε-algorithme, C. R. Acad. Sci. Paris Sér. A 275 (1972), 1351-1353.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-zmv24i3p299bwm
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.