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Journal of Complex Analysis
Volume 2018 (2018), Article ID 7289092, 11 pages
https://doi.org/10.1155/2018/7289092
Research Article

Fixed Point and Newton’s Methods in the Complex Plane

Département de Mathématiques, Faculté des Sciences, Université de Sherbrooke, 2500 Boul. de l’Université, Sherbrooke, QC, Canada J1K 2R1

Correspondence should be addressed to Calvin Gnang

Received 29 August 2017; Accepted 12 December 2017; Published 29 January 2018

Academic Editor: Daniel Girela

Copyright © 2018 François Dubeau and Calvin Gnang. 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. F. Dubeau and C. Gnang, “Fixed point and Newton's methods for solving a nonlinear equation: from linear to high-order convergence,” SIAM Review, vol. 56, no. 4, pp. 691–708, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  2. F. Dubeau, “Polynomial and rational approximations and the link between Schröder's processes of the first and second kind,” Abstract and Applied Analysis, vol. 2014, Article ID 719846, 5 pages, 2014. View at Publisher · View at Google Scholar · View at Scopus
  3. F. Dubeau, “On comparisons of chebyshev-halley iteration functions based on their asymptotic constants,” International Journal of Pure and Applied Mathematics, vol. 85, no. 5, pp. 965–981, 2013. View at Publisher · View at Google Scholar · View at Scopus
  4. E. Schröder, “Ueber unendlich viele algorithmen zur auflösung der gleichungen,” Mathematische Annalen, vol. 2, no. 2, pp. 317–365, 1870. View at Publisher · View at Google Scholar · View at MathSciNet
  5. E. Schröder, “On Infinitely Many Algorithms for Solving Equations,” in Institute for advanced Computer Studies, G. W. Stewart, Ed., pp. 92–121, University of Maryland, 1992. View at Google Scholar
  6. J. F. Traub, Iterative Methods for the Solution of Equations, Prentice-Hall, NJ, USA, Englewood Cliffs, 1964.
  7. A. S. Householder, The Numerical Treatment of a Single Nonlinear Equation, McGraw-Hill Book Co., NY, USA, 1970. View at MathSciNet
  8. E. Bodewig, “On types of convergence and on the behavior of approximations in the neighborhood of a multiple root of an equation,” Quarterly of Applied Mathematics, vol. 7, pp. 325–333, 1949. View at Publisher · View at Google Scholar · View at MathSciNet
  9. M. Shub and S. Smale, “Computational complexity. On the geometry of polynomials and a theory of cost,” Annales Scientifiques de l'École Normale Supérieure. Quatrième Série, vol. 18, no. 1, pp. 107–142, 1985. View at Google Scholar · View at MathSciNet
  10. M. Petković and D. Herceg, “On rediscovered iteration methods for solving equations,” Journal of Computational and Applied Mathematics, vol. 107, no. 2, pp. 275–284, 1999. View at Publisher · View at Google Scholar · View at MathSciNet
  11. J. Gerlach, “Accelerated convergence in Newton's method,” SIAM Review, vol. 36, no. 2, pp. 272–276, 1994. View at Publisher · View at Google Scholar · View at Scopus
  12. W. F. Ford and J. A. Pennline, “Accelerated convergence in Newton's method,” SIAM Review, vol. 38, no. 4, pp. 658-659, 1996. View at Publisher · View at Google Scholar · View at Scopus
  13. F. Dubeau, “On the modified Newton's method for multiple root,” Journal of Mathematical Analysis, vol. 4, no. 2, pp. 9–15, 2013. View at Google Scholar · View at MathSciNet
  14. J. L. Varona, “Graphic and numerical comparison between iterative methods,” The Mathematical Intelligencer, vol. 24, no. 1, pp. 37–46, 2002. View at Publisher · View at Google Scholar · View at MathSciNet