On the derivation of higher order root-finding methods

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

2 Scopus citations


High order root-finding algorithms are constructed based on some canonical conditions and a generalized Taylor series. The convergence order is automatically determined using these canonical conditions. The proposed approaches resulted in deriving methods of any desired order including the Newton, Halley, and Ostrowski iterations. It is also shown that, when zeros are simple, higher order methods may be obtained by applying lower order methods such as Newton Iteration to new functions which have same zeros as the original function. These functions are constructed so that the first few derivatives beyond the first vanish. Several examples are given for constructing methods of higher order for computing the zeros of the entire function sin(z).

Original languageEnglish (US)
Title of host publicationProceedings of the 2007 American Control Conference, ACC
Number of pages6
StatePublished - Dec 1 2007
Event2007 American Control Conference, ACC - New York, NY, United States
Duration: Jul 9 2007Jul 13 2007

Publication series

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


Other2007 American Control Conference, ACC
Country/TerritoryUnited States
CityNew York, NY


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


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