Numerical Algorithms

, Volume 61, Issue 3, pp 397–412 | Cite as

Secant-type methods and nondiscrete induction

Original Paper


The celebrated nondiscrete mathematical induction has been used to improve error bounds of distances involved in the discrete case but not the sufficient convergence conditions for Secant–type methods. We show that using the same information as before, the following advantages can be obtained: weaker sufficient convergence conditions; tighter error bounds on the distances involved and a more precise information on the location of the solution. Numerical examples validating the theoretical conclusions are also provided in this study.


Secant–type methods Banach space Nondiscrete mathematical induction Semilocal convergence Traub’s method Consistent approximation Rate of convergence 

AMS 2000 Subject Classifications

65H10 65B05 65G99 65N30 47H17 49M15 


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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Department of Mathematics SciencesCameron UniversityLawtonUSA
  2. 2.Laboratoire de Mathématiques et ApplicationsPoitiers UniversityFuturoscope Chasseneuil CedexFrance

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