Some improvements of Jarratt’s method with sixth-order convergence. (English) Zbl 1122.65329

Summary: We present a one-parameter family of variants of Jarratt’s fourth-order method for solving nonlinear equations. It is shown that the order of convergence of each family member is improved from four to six even though it adds one evaluation of the function at the point iterated by Jarratt’s method per iteration. Several numerical examples are given to illustrate the performance of the presented methods.


65H05 Numerical computation of solutions to single equations
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[1] Ostrowski, A. M., Solution of equations in Euclidean and Banach space (1973), Academic Press: Academic Press New York · Zbl 0304.65002
[2] Grau, M., An improvement to the computing of nonlinear equation solutions, Numer. Algorithms, 34, 1-12 (2003) · Zbl 1043.65071
[3] Grau, M.; Díaz-Barrero, J. L., An improvement to Ostrowski root-finding method, J. Math. Anal. Appl., 173, 450-456 (2006) · Zbl 1090.65053
[4] Grau, M.; Díaz-Barrero, J. L., An improvement of the Euler-Chebyshev iterative method, J. Math. Anal. Appl., 315, 1-7 (2006) · Zbl 1113.65048
[8] Argyros, I. K.; Chen, D.; Qian, Q., The Jarratt method in Banach space setting, J. Comput. Appl. Math., 51, 103-106 (1994) · Zbl 0809.65054
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