Derivative-free family of higher order root finding methods

Research output: Chapter in Book/Report/Conference proceedingConference contribution

5 Scopus citations


Most higher order root finding methods require evaluation of a function and/or its derivatives at one or multiple points. There are cases where the derivatives of a given function are costly to compute. In this paper, higher order methods which do not require computation of any derivatives are derived. Asymptotic analysis has shown that these methods are approximations of root iterations. One of the main features of the proposed approaches is that one can develop multi-point derivative-free methods of any desired order. For lower order methods, these correspond to the Newton, and Ostrowski iterations. Several examples involving polynomials and entire functions have shown that the proposed methods can be applied to polynomial and non-polynomial equations.

Original languageEnglish (US)
Title of host publication2009 American Control Conference, ACC 2009
Number of pages6
StatePublished - Nov 23 2009
Event2009 American Control Conference, ACC 2009 - St. Louis, MO, United States
Duration: Jun 10 2009Jun 12 2009

Publication series

NameProceedings of the American Control Conference
ISSN (Print)0743-1619


Other2009 American Control Conference, ACC 2009
Country/TerritoryUnited States
CitySt. Louis, MO


  • Derivative free methods
  • Halley's method
  • Higher order methods
  • Newton's method
  • Order of convergence
  • Ostrowski method
  • Root iterations
  • Root-finding
  • Square root iteration
  • Zeros of analytic functions
  • Zeros of polynomials


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