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2012 Computing Simple Roots by an Optimal Sixteenth-Order Class
F. Soleymani, S. Shateyi, H. Salmani
J. Appl. Math. 2012(SI06): 1-13 (2012). DOI: 10.1155/2012/958020


The problem considered in this paper is to approximate the simple zeros of the function f ( x ) by iterative processes. An optimal 16th order class is constructed. The class is built by considering any of the optimal three-step derivative-involved methods in the first three steps of a four-step cycle in which the first derivative of the function at the fourth step is estimated by a combination of already known values. Per iteration, each method of the class reaches the efficiency index 16 5 1.741 , by carrying out four evaluations of the function and one evaluation of the first derivative. The error equation for one technique of the class is furnished analytically. Some methods of the class are tested by challenging the existing high-order methods. The interval Newton's method is given as a tool for extracting enough accurate initial approximations to start such high-order methods. The obtained numerical results show that the derived methods are accurate and efficient.


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F. Soleymani. S. Shateyi. H. Salmani. "Computing Simple Roots by an Optimal Sixteenth-Order Class." J. Appl. Math. 2012 (SI06) 1 - 13, 2012.


Published: 2012
First available in Project Euclid: 3 January 2013

zbMATH: 1268.65070
MathSciNet: MR2997247
Digital Object Identifier: 10.1155/2012/958020

Rights: Copyright © 2012 Hindawi


Vol.2012 • No. SI06 • 2012
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