Numerische Mathematik

, Volume 46, Issue 3, pp 323–337

Attractive cycles in the iteration of meromorphic functions

  • James Lucien Howland
  • Rémi Vaillancourt

DOI: 10.1007/BF01389489

Cite this article as:
Howland, J.L. & Vaillancourt, R. Numer. Math. (1985) 46: 323. doi:10.1007/BF01389489


The existence of attractive cycles constitutes a serious impediment to the solution of nonlinear equations by iterative methods. This problem is illustrated in the case of the solution of the equationz tanz=c, for complex values ofc, by Newton's method. Relevant results from the theory of the iteration of rational functions are cited and extended to the analysis of this case, in which a meromorphic function is iterated. Extensive numerical results, including many attractive cycles, are summarized.

Subject Classifications

AMS(MOS): 30D05, 30-04, 65E05, 65H05CR: 5.15

Copyright information

© Springer-Verlag 1985

Authors and Affiliations

  • James Lucien Howland
    • 1
  • Rémi Vaillancourt
    • 1
  1. 1.Department of MathematicsUniversity of OttawaOttawaCanada