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http://dx.doi.org/10.14403/jcms.2014.27.4.753

A SEXTIC-ORDER SIMPLE-ROOT FINDER WITH RATIONAL WEIGHTING FUNCTIONS OF DERIVATIVE-TO-DERIVATIVE RATIOS  

Kim, Young Ik (Department of Applied Mathematics Dankook University)
Publication Information
Journal of the Chungcheong Mathematical Society / v.27, no.4, 2014 , pp. 753-762 More about this Journal
Abstract
A three-step sextic simple-root finder is constructed with the use of weighting functions of derivative-to-derivative ratios. Their convergence and computational properties are investigated along with concrete numerical examples to verify the theoretical analysis.
Keywords
Sextic-order convergence; asymptotic error constant; efficiency index; Jarratt-like;
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1 L. V. Ahlfors, Complex Analysis, McGraw-Hill Book, Inc, 1979.
2 I. K. Argyros, D. Chen, and Q. Qian, The Jarratt method in Banach space setting, J. Comput. Appl. Math. 51 (1994), 103-106.   DOI   ScienceOn
3 W. Bi, Q. Wu, and H. Ren, A new family of eighth-order iterative methods for solving nonlinear equations, Appl. Math. Comput. 214 (2009), no. 4, 236-245.   DOI   ScienceOn
4 C. Chun, Certain improvements of Chebyshev-Halley methods with accelerated fourth-order convergence, Appl. Math. Comput. 189 (2007), 597-601.   DOI   ScienceOn
5 C. Chun, Some improvements of Jarratts method with sixth-order convergence, Appl. Math. Comput. 190 (2007), 1432-1437.   DOI   ScienceOn
6 L. Fanga, T. Chen, L. Tian, L. Sun, and B. Chen, A modi ed Newton-type method with sixth-order convergence for solving nonlinear equations, Procedia Engineering 15 (2011), 3124-3128.   DOI   ScienceOn
7 Y. H. Geum and Y. I. Kim, A biparametric family of four-step sixteenth-order root- nding methods with the optimal eciency index, Appl. Math. Lett. 24 (2011), 1336-1342.   DOI   ScienceOn
8 P. Jarratt, Multipoint iterative methods for solving certain equations, The Computer Journal 8 (1966), no. 4, 398-400.
9 Y. I. Kim, A new two-step biparametric family of sixth-order iterative methods free from second derivatives for solving nonlinear algebraic equations, Appl. Math. Comput. 215 (2010), 3418-3424.   DOI   ScienceOn
10 S. K. Parhi and D. K. Gupta, A sixth order method for nonlinear equations, Appl. Math. Comput. 203 (2008), 50-55.   DOI   ScienceOn
11 Y. Peng, H. Feng, Q. Li, and X. Zhang, A fourth-order derivative-free algorithm for nonlinear equations, J. Comput. Appl. Math. 235 (2011), 2551-2559.   DOI   ScienceOn
12 X. Wang, J. Kou, and Y. Li, A variant of Jarratt method with sixth-order convergence, Appl. Math. Comput. 204 (2008), 14-19.   DOI   ScienceOn
13 B. V. Shabat, Introduction to Complex Analysis PART II, Functions of Several Variables, American Mathematical Society (1992).
14 F. Soleymani, Regarding the accuracy of optimal eighth-order methods, Math. Comput. Model. 53 (2011), 5-6, 1351-1357.
15 J. F. Traub, Iterative Methods for the Solution of Equations, Chelsea Publishing Company (1982).
16 S. Wolfram, The Mathematica Book(5th ed.), Wolfram Media, 2003.