Table of Contents Author Guidelines Submit a Manuscript
Discrete Dynamics in Nature and Society
Volume 2006 (2006), Article ID 52682, 15 pages
http://dx.doi.org/10.1155/DDNS/2006/52682

Conjugate gradient algorithm and fractals

Département de Mathématiques, Université Badji-Mokhtar, B.P. 12, Annaba 23.000, Algeria

Received 31 August 2005; Accepted 28 November 2005

Copyright © 2006 Mohamed Lamine Sahari and Ilhem Djellit. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. M. Al-Baali, “Descent property and global convergence of the Fletcher-Reeves method with inexact line search,” IMA Journal of Numerical Analysis, vol. 5, no. 1, pp. 121–124, 1985. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. A. Cayley, “Desiderata and suggestions: no. 3. The Newton-Fourier imaginary problem,” American Journal of Mathematics, vol. 2, no. 1, p. 97, 1879. View at Publisher · View at Google Scholar · View at MathSciNet
  3. K. Falconer, Fractal Geometry, Mathematical Foundations and Applications, John Wiley & Sons, Chichester, 1990. View at MathSciNet
  4. R. Fletcher, “A new approach to variable metric algorithms,” The Computer Journal, vol. 13, no. 3, pp. 317–322, 1970. View at Publisher · View at Google Scholar
  5. R. Fletcher and M. J. D. Powell, “A rapidly convergent descent method for minimization,” The Computer Journal, vol. 6, pp. 163–168, 1963/1964. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. G. Julia, “Mémoire sur l'itération des fonctions rationnelles,” Journal de Mathématiques Pures et Appliquées, vol. 81, pp. 47–235, 1918. View at Google Scholar
  7. B. B. Mandelbrot, The Fractal Geometry of Nature, W. H. Freeman, New York, 1983.
  8. J. Nocedal, “Theory of algorithms for unconstrained optimization,” in Acta Numerica, 1992, Acta Numer., pp. 199–242, Cambridge University Press, Cambridge, 1992. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. E. Polak, Computational Methods in Optimization. A Unified Approach, vol. 77 of Mathematics in Science and Engineering, Academic Press, New York, 1971. View at MathSciNet
  10. G. Zoutendijk, “Nonlinear programming, computational methods,” in Integer and Nonlinear Programming, J. Abadie, Ed., pp. 37–86, North-Holland, Amsterdam, 1970. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet