Accurate fourteenthorder methods for solving nonlinear equations
 Parviz Sargolzaei,
 Fazlollah Soleymani
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We establish new iterative methods of local order fourteen to approximate the simple roots of nonlinear equations. The considered threestep eighthorder construction can be viewed as a variant of Newton’s method in which the concept of Hermite interpolation is used at the third step to reduce the number of evaluations. This scheme includes three evaluations of the function and one evaluation of the first derivative per iteration, hence its efficiency index is 1.6817. Next, the obtained approximation for the derivative of the Newton’s iteration quotient is again taken into consideration to furnish novel fourteenthorder techniques consuming four function and one first derivative evaluations per iteration. In providing such new fourteenthorder methods, we also take a special heed to the computational burden. The contributed fourstep methods have 1.6952 as their efficiency index. Finally, various numerical examples are given to illustrate the accuracy of the developed techniques.
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 Title
 Accurate fourteenthorder methods for solving nonlinear equations
 Journal

Numerical Algorithms
Volume 58, Issue 4 , pp 513527
 Cover Date
 20111201
 DOI
 10.1007/s1107501194674
 Print ISSN
 10171398
 Online ISSN
 15729265
 Publisher
 Springer US
 Additional Links
 Topics
 Keywords

 Nonlinear equations
 Threestep methods
 Fourstep methods
 Efficiency index
 Order of convergence
 Simple root
 65H05
 65B99
 Industry Sectors
 Authors

 Parviz Sargolzaei ^{(1)}
 Fazlollah Soleymani ^{(2)}
 Author Affiliations

 1. Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran
 2. Young Researchers Club, Zahedan Branch, Islamic Azad University, Zahedan, Iran