Some convergence acceleration processes for a class of vector sequences

G. Sedogbo

Applicationes Mathematicae (1997)

  • Volume: 24, Issue: 3, page 299-306
  • ISSN: 1233-7234

Abstract

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Let ( S n ) be some vector sequence, converging to S, satisfying S n - S ϱ n n θ ( β 0 + β 1 n - 1 + β 2 n - 2 + . . . ) , 0 | ϱ | 1 , θ 0 , where β 0 ( 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.

How to cite

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Sedogbo, G.. "Some convergence acceleration processes for a class of vector sequences." Applicationes Mathematicae 24.3 (1997): 299-306. <http://eudml.org/doc/219171>.

@article{Sedogbo1997,
abstract = {Let $(S_n)$ be some vector sequence, converging to S, satisfying $S_n - S \sim ϱ ^n n^\{θ\}(β_0 + β_1 n^\{-1\} + β_2 n^\{-2\} + ...), 0 |ϱ|1 , θ 0$, 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.},
author = {Sedogbo, G.},
journal = {Applicationes Mathematicae},
keywords = {convergence acceleration; vector extrapolation methods; vector sequences; iterative methods; Aitken's method; numerical examples; Newton's method; vector epsilon method},
language = {eng},
number = {3},
pages = {299-306},
title = {Some convergence acceleration processes for a class of vector sequences},
url = {http://eudml.org/doc/219171},
volume = {24},
year = {1997},
}

TY - JOUR
AU - Sedogbo, G.
TI - Some convergence acceleration processes for a class of vector sequences
JO - Applicationes Mathematicae
PY - 1997
VL - 24
IS - 3
SP - 299
EP - 306
AB - Let $(S_n)$ be some vector sequence, converging to S, satisfying $S_n - S \sim ϱ ^n n^{θ}(β_0 + β_1 n^{-1} + β_2 n^{-2} + ...), 0 |ϱ|1 , θ 0$, 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.
LA - eng
KW - convergence acceleration; vector extrapolation methods; vector sequences; iterative methods; Aitken's method; numerical examples; Newton's method; vector epsilon method
UR - http://eudml.org/doc/219171
ER -

References

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  2. [2] S. Bhowmick, R. Bhattacharya and D. Roy, Iterations of convergence accelerating nonlinear transforms, Comput. Phys. Comm. 54 (1989), 31-46. Zbl0798.65006
  3. [3] C. Brezinski, Algorithmes d'Accélération de la Convergence, Etude Numérique, Editions Technip, Paris, 1978. Zbl0396.65001
  4. [4] C. Brezinski and M. Redivo Zaglia, Extrapolation Methods. Theory and Practice, Math. Stud. in Comput. Math. 2, North-Holland, 1991. 
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  6. [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. [7] N. Osada, Extensions of Levin's transformations to vector sequences, Numer. Algorithms 2 (1992), 121-132. Zbl0759.65001
  8. [8] L. B. Rall, Convergence of the Newton process to multiple solutions, Numer. Math. 9 (1966), 23-37. 
  9. [9] G. W. Reddien, Newton's method and high order singularities, Comput. Math. Appl. 5 (1979), 79-86. Zbl0436.65032
  10. [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. [11] J. Wimp, Sequence Transformations and their Applications, Academic Press, New York, 1981. Zbl0566.47018
  12. [12] P. Wynn, Acceleration techniques for iterated vector and matrix problems, Math. Comp. 16 (1962), 301-322. Zbl0105.10302
  13. [13] P. Wynn, Transformations de séries à l'aide de l'ε-algorithme, C. R. Acad. Sci. Paris Sér. A 275 (1972), 1351-1353. Zbl0257.65005

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