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International Journal of Mathematics and Mathematical Sciences
Volume 2006, Article ID 36482, 9 pages
http://dx.doi.org/10.1155/IJMMS/2006/36482

On the convergence of a Newton-like method in n and the use of Berinde's exit criterion

1Department of Applied Mathematics, University College of Science, 92 A.P.C. Road, Calcutta 700009, India
2Department of Mathematics, University of Kalyani, Kalyani 741 235, West Bengal, India

Received 1 January 2006; Revised 11 August 2006; Accepted 21 August 2006

Copyright © 2006 Hindawi Publishing Corporation. 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. V. Berinde, “An extension of the Newton-Raphson method for solving non-linear equations,” in Proceedings of the International Scientific Conference MICROCAD-SYSTEMS, pp. 63–64, Technical University, Kösice, 1993. View at Google Scholar
  2. V. Berinde, “On some exit criteria for the Newton method,” Novi Sad Journal of Mathematics, vol. 27, no. 1, pp. 19–26, 1997. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. V. Berinde, “On the convergence of the Newton method,” Transactions of the Technical University of Kosice, no. 1, pp. 68–77, 1997. View at Google Scholar
  4. V. Berinde, “On the extended Newton's method,” in Advances in Difference Equations, S. Elaydi, I. Györi, and G. Ladas, Eds., pp. 81–88, Gordon and Breach, Amsterdam, 1997. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. H. B. Keller, “Newton's method under mild differentiability conditions,” Journal of Computer and System Sciences, vol. 4, no. 1, pp. 15–28, 1970. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. J. M. Ortega and W. C. Rheinboldt, Iterative Solution of Nonlinear Equations in Several Variables, Academic Press, New York, 1970. View at Zentralblatt MATH · View at MathSciNet
  7. R. Sen, “A modification of the Newton-Kantorovitch method,” Mathematica (Cluj), vol. 8 (31), pp. 155–161, 1966. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. R. Sen, “On a variant of Newton's method under relaxed differentiability conditions,” Bulletin Mathématique de la Société des Sciences Mathématiques de la R. S. Roumanie, vol. 22(70), no. 1, pp. 87–93, 1978. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. R. Sen, A. Biswas, R. Patra, and S. Mukherjee, “An extension on Berinde's criterion for the convergence of a Newton-like method,” to appear in Bulletin of the Calcutta Mathematical Society.
  10. R. Sen and P. Guhathakurta, “On a variant of Ball Newton method under relaxed differentiability condition,” Soochow Journal of Mathematics, vol. 19, no. 2, pp. 199–211, 1993. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. M. M. Vainberg, Variational Methods for the Study of Nonlinear Operators, Holden-day, California, 1964, with a chapter on Newton's method by L. V. Kantorovich and G. P. Akilov. View at Zentralblatt MATH · View at MathSciNet
  12. R. S. Varga, Matrix Iterative Analysis, Prentice-Hall, New Jersey, 1962. View at Zentralblatt MATH · View at MathSciNet