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Zbl 1215.65093
Geum, Young Hee; Kim, Young Ik
A biparametric family of optimally convergent sixteenth-order multipoint methods with their fourth-step weighting function as a sum of a rational and a generic two-variable function. (English)
[J] J. Comput. Appl. Math. 235, No. 10, 3178-3188 (2011). ISSN 0377-0427

Authors' abstract: A biparametric family of four-step multipoint iterative methods of order sixteen to numerically solve nonlinear equations are developed and their convergence properties are investigated. The efficiency indices of these methods are all found to be $16^{1/5}\approx 1.741101$, being optimally consistent with the conjecture of Kung-Traub. Numerical examples as well as comparison with existing methods developed by Kung-Traub and Neta are demonstrated to confirm the developed theory in this paper.
[Costică Moroşanu (Iaşi)]

MSC 2000:: *65H05 Single nonlinear equations (numerical methods)
65H99 Nonlinear algebraic or transcendental equations

Keywords: eighth-order; sixteenth-order; optimal order; biparametric family; asymptotic error constant; efficiency index; four-step multipoint iterative methods; nonlinear equations; convergence

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Zentralblatt MATH Berlin [Germany]