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A modified Newton-Jarratt’s composition. (English) Zbl 1251.65074
Summary: A reduced composition technique is used on Newton and Jarratt’s methods in order to obtain an optimal relation between convergence order, functional evaluations and number of operations. Following this aim, a family of methods is obtained whose efficiency indices are proved to be better for systems of nonlinear equations.

MSC:
65H10 Numerical computation of solutions to systems of equations
65H05 Numerical computation of solutions to single equations
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[1] Cordero, A., Torregrosa, J.R.: Variants of Newton’s method using fifth-order quadrature formulas. Appl. Math. Comput. 190, 686–698 (2007) · Zbl 1122.65350
[2] Cordero, A., Torregrosa, J.R.: On interpolation variants of Newton’s method. In: Proceedings of the 2th International Conference on Approximation Methods and Numerical Modelling in Environment and Natural Resources. Universidad de Granada (Spain), 11–13 July 2007, ISBN: 978-84-338-4782-9.
[3] Frontini, M., Sormani, E.: Third-order methods from quadrature formulae for solving systems of nonlinear equations. Appl. Math. Comput. 149, 771–782 (2004) · Zbl 1050.65055
[4] Jarrat, P.: Some fourth order multipoint iterative methods for solving equations. Math. Comput. 20, 434–437 (1966) · Zbl 0229.65049
[5] Gerlach, J.: Accelerated convergence in Newton’s method. SIAM Rev. 36(2), 272–276 (1994) · Zbl 0814.65046
[6] Nedzhibov, G.H.: A family of multi-point iterative methods for solving systems of nonlinear equations. J. Comput. Appl. Math. doi: 10.1016/j.cam.2007.10.054 (2008) · Zbl 1154.65037
[7] Ozban, A.Y.: Some new variants of Newton’s method. Appl. Math. Lett. 17, 677–682 (2004) · Zbl 1065.65067
[8] Ostrowski, A.M.: Solutions of Equations and Systems of Equations. Academic, New York (1966) · Zbl 0222.65070
[9] Romero Alvarez, N., Ezquerro, J.A., Hernandez, M.A.: Aproximación de soluciones de algunas equacuaciones integrales de Hammerstein mediante métodos iterativos tipo Newton. XXI Congreso de ecuaciones diferenciales y aplicaciones, Universidad de Castilla-La Mancha (2009)
[10] Traub, J.F.: Iterative Methods for the Solution of Equations. Chelsea, New York (1982) · Zbl 0472.65040
[11] Wang, X., Kou, J., Li, Y.: Modified Jarratt method with sixth-order convergence. Appl. Math. Lett. 22, 1798–1802 (2009) · Zbl 1184.65054
[12] Weerakoon, S., Fernando, T.G.I.: A variant of Newton’s method with accelerated third-order convergence. Appl. Math. Lett. 13(8), 87–93 (2000) · Zbl 0973.65037
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