Paper Info

Title | ||
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On second derivative-free zero finding methods |

Abstract | ||
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High order root-finding algorithms are constructed from formulas for approximating higher order logarithmic and standard derivatives. These formulas are free of derivatives of second order or higher and use only function evaluation and/or first derivatives at multiple points. Richardson extrapolation technique is applied to obtain better approximations of these derivatives. The proposed approaches resulted in deriving a family of root-finding methods of any desired order. The first member of this family is the square root iteration or Ostrowski iteration. Additionally, higher order derivatives are approximated using multi-point function evaluations. We also derived a procedure for fourth order methods that are dependents only on the function and its first derivative evaluated at multiple points. |

Year | DOI | Venue |
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2010 | 10.1109/ACC.2010.5531432 | American Control Conference |

Keywords | DocType | ISSN |

iterative methods,polynomials,ostrowski iteration,richardson extrapolation,derivative free zero finding methods,root-finding algorithms,square root iteration,halley's method,newton's method,ostrowski method,root iterations,zeros of analytic functions,zeros of polynomials,derivative free methods,higher order methods,order of convergence,root-finding,extrapolation,second order,newton s method,convergence,higher order,analytic function,halley s method,root finding,taylor series,newton method | Conference | 0743-1619 |

ISBN | Citations | PageRank |

978-1-4244-7426-4 | 0 | 0.34 |

References | Authors | |

2 | 1 |

Authors (1 rows)

Cited by (0 rows)

References (2 rows)

Name | Order | Citations | PageRank |
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Hasan, M.A. | 1 | 0 | 0.34 |