An improvement of Chebyshev–Halley methods free from second derivative

In this paper, a family of modified Chebyshev–Halley’s methods free from second derivative is presented. Per iteration the new methods require three evaluations of the function and one of its first derivatives. A detailed convergence analysis of the new methods shows that the new methods are at leas...

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Bibliographic Details
Published in:Applied mathematics and computation 2014-05, Vol.235, p.221-225
Main Authors: Li, Dingfang, Liu, Ping, Kou, Jisheng
Format: Article
Language:English
Subjects:
Chebyshev approximation
Chebyshev–Halley method
Computation
Convergence
Derivatives
Iterative method
Iterative methods
Mathematical analysis
Mathematical models
Newton method
Non-linear equations
Root-finding
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Summary:In this paper, a family of modified Chebyshev–Halley’s methods free from second derivative is presented. Per iteration the new methods require three evaluations of the function and one of its first derivatives. A detailed convergence analysis of the new methods shows that the new methods are at least fifth-order convergent and especially, the modified super-Halley’s method is sixth-order convergent. Numerical examples are given to illustrate the efficiency and performance of the new methods.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2014.02.083