# Some convergence acceleration processes for a class of vector sequences

Applicationes Mathematicae (1997)

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

## Access Full Article

top## Abstract

top## How to cite

topSedogbo, 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

top- [1] A. C. Aitken, On Bernoulli's numerical solution of algebraic equations, Proc. Roy. Soc. Edinburgh 46 (1926), 289-305. Zbl52.0098.05
- [2] S. Bhowmick, R. Bhattacharya and D. Roy, Iterations of convergence accelerating nonlinear transforms, Comput. Phys. Comm. 54 (1989), 31-46. Zbl0798.65006
- [3] C. Brezinski, Algorithmes d'Accélération de la Convergence, Etude Numérique, Editions Technip, Paris, 1978. Zbl0396.65001
- [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. Zbl0765.65004
- [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. Zbl0759.65001
- [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. Zbl0436.65032
- [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. Zbl0566.47018
- [12] P. Wynn, Acceleration techniques for iterated vector and matrix problems, Math. Comp. 16 (1962), 301-322. Zbl0105.10302
- [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

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.