On Henrici's transformation in optimization

B. Rhanizar

Applicationes Mathematicae (2000)

  • Volume: 27, Issue: 2, page 127-141
  • ISSN: 1233-7234

Abstract

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Henrici’s transformation is a generalization of Aitken’s Δ 2 -process to the vector case. It has been used for accelerating vector sequences. We use a modified version of Henrici’s transformation for solving some unconstrained nonlinear optimization problems. A convergence acceleration result is established and numerical examples are given.

How to cite

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Rhanizar, B.. "On Henrici's transformation in optimization." Applicationes Mathematicae 27.2 (2000): 127-141. <http://eudml.org/doc/219262>.

@article{Rhanizar2000,
abstract = {Henrici’s transformation is a generalization of Aitken’s $Δ^2$-process to the vector case. It has been used for accelerating vector sequences. We use a modified version of Henrici’s transformation for solving some unconstrained nonlinear optimization problems. A convergence acceleration result is established and numerical examples are given.},
author = {Rhanizar, B.},
journal = {Applicationes Mathematicae},
keywords = {Henrici's transformation; nonlinear optimization; unconstrained nonlinear optimization; convergence acceleration},
language = {eng},
number = {2},
pages = {127-141},
title = {On Henrici's transformation in optimization},
url = {http://eudml.org/doc/219262},
volume = {27},
year = {2000},
}

TY - JOUR
AU - Rhanizar, B.
TI - On Henrici's transformation in optimization
JO - Applicationes Mathematicae
PY - 2000
VL - 27
IS - 2
SP - 127
EP - 141
AB - Henrici’s transformation is a generalization of Aitken’s $Δ^2$-process to the vector case. It has been used for accelerating vector sequences. We use a modified version of Henrici’s transformation for solving some unconstrained nonlinear optimization problems. A convergence acceleration result is established and numerical examples are given.
LA - eng
KW - Henrici's transformation; nonlinear optimization; unconstrained nonlinear optimization; convergence acceleration
UR - http://eudml.org/doc/219262
ER -

References

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  1. [1] A. Auslender, Optimisation: Méthodes Numériques, Masson, Paris, 1976. Zbl0326.90057
  2. [2] C. Brezinski, Accélération de la Convergence en Analyse Numérique, Springer, Berlin, 1977. Zbl0352.65003
  3. [3] C. Brezinski, Algorithmes d'Accélération de la Convergence, Etude Numérique, Editions Technip, Paris, 1978. Zbl0396.65001
  4. [4] P. G. Ciarlet, Introduction à l'Analyse Numérique Matricielle et à l'Optimisation, Masson, Paris, 1985. Zbl0488.65001
  5. [5] J. E. Dennis, Jr. and R. B. Schnabel, Numerical Methods For Unconstrained Optimization and Nonlinear Equations, Prentice-Hall, Englewood Cliffs, NJ, 1983. 
  6. [6] I. Gohberg and S. Golderg, Basic Operator Theory, Birkhäuser, Basel, 1981. 
  7. [7] P. Henrici, Elements of Numerical Analysis, Wiley, New York, 1964. Zbl0149.10901
  8. [8] A. Kolmogorov et S. Fomine, Eléments de la Théorie des Fonctions et de l'Analyse Fonctionnelle, Editions Mir, Moscou, 1979. 
  9. [9] H. Le Ferrand, Recherche d'extrema par les méthodes d'extrapolation, C. R. Acad. Sci. Paris Sér. I 318 (1994), 1043-1049. 
  10. [10] B. Rhanizar, On extrapolation methods in optimization, Appl. Numer. Math. 25 (1997), 485-498. Zbl0888.65070
  11. [11] H. Sadok, Accéleration de la convergence de suites vectorielles et méthodes point fixe, Thèse, Université des Sciences et Techniques de Lille, 1988. 
  12. [12] J. Vignes, Algorithmes Numériques, Analyse et Mise en Œuvre, Vol. 2, Editions Technip, Paris, 1980. 

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