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Zbl 1180.65058
Thukral, R.; Petković, M.S.
A family of three-point methods of optimal order for solving nonlinear equations. (English)
[J] J. Comput. Appl. Math. 233, No. 9, 2278-2284 (2010). ISSN 0377-0427

Summary: A family of three-point iterative methods for solving nonlinear equations is constructed using a suitable parametric function and two arbitrary real parameters. It is proved that these methods have the convergence order eight requiring only four function evaluations per iteration. In this way, it is demonstrated that the proposed class of methods supports the Kung-Traub hypothesis [{\it H. T. Kung} and {\it J. F. Traub}, J. Assoc. Comput. Mach. 21, 643--651 (1974; Zbl 0289.65023)] on the upper bound $2^n$ of the order of multipoint methods based on $n+1$ function evaluations. Consequently, this class of root solvers possesses very high computational efficiency. Numerical examples are included to demonstrate exceptional convergence speed with only few function evaluations.

MSC 2000:: *65H05 Single nonlinear equations (numerical methods)

Keywords: multipoint iterative methods; nonlinear equations; optimal order of convergence; computational efficiency

Citations: Zbl 0289.65023

Cited in: Zbl 1210.65100

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