Numerical Algorithms

, Volume 69, Issue 2, pp 443–453 | Cite as

Always convergent iteration methods for nonlinear equations of Lipschitz functions

  • A. Galántai
  • J. Abaffy
Original Paper


We define a class of always convergent methods for solving nonlinear equations of real Lipschitz functions. These methods generate monotone iterations that either converge to the nearest zero, if exists or leave the interval in a finite number of steps. We also investigate the speed and relative speed of these methods and show that no optimal method exists in the class. After deriving special cases we report on numerical testing that show the feasibility of these methods.


Monotone convergence Lipschitz functions Convergence speed 

Mathematics Subject Classifications (2010)

65H05 65H20 47H10 


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Óbuda UniversityBudapestHungary

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