On a novel optimal quartically class of methods. (English) Zbl 1252.41015

Summary: Following the existing trend in providing optimal derivative-free methods for finding simple roots; this paper suggests a general class of two-step iteration methods, which are consistent with the optimality conjecture of H. T. Kung and J. F. Traub [J. Assoc. Comput. Mach. 21, 643–651 (1974; Zbl 0289.65023)] for constructing multi-point iterative without memory methods. The theoretical results show the fourth-order convergence using only three evaluations of the function per full cycle. Our developed class of iterations is totally free from derivative evaluation, which is so much fruitful for engineering and optimization problems.


41A25 Rate of convergence, degree of approximation
65B99 Acceleration of convergence in numerical analysis
65H05 Numerical computation of solutions to single equations


Zbl 0289.65023
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