IJPAM: Volume 72, No. 1 (2011)

ON A BI-PARAMETRIC CLASS OF OPTIMAL
EIGHTH-ORDER DERIVATIVE-FREE METHODS

F. Soleymani
Young Researchers Club
Islamic Azad University
Zahedan Branch, Zahedan, IRAN


Abstract. This paper proposes a novel class of three-step without memory iterations including two free parameters. The suggested bi-parametric class of methods needs four function evaluations per iteration and it also supports the optimality conjecture of Kung and Traub [6] for constructing multi-point iterations without memory. Our class can be viewed as the generalization of the two-step derivative-free family of Ren et al. [8]. The analytical proof of the proposed derivative-free class is given. And finally, numerical examples are employed to corroborate the underlying theory developed in this contribution.

Received: May 30, 2011

AMS Subject Classification: 65H05

Key Words and Phrases: nonlinear scalar equations, optimality, order of convergence, derivative-free methods, simple root, without memory iterations

Download paper from here.



Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2011
Volume: 72
Issue: 1