New variants of Jarratt's method with sixth-order convergence (Q1047172)

The authors propose some new variants of the Jarratt method with sixth-order convergence for solving univariate nonlinear equations. \textit{P. Jarratt} modified the Newton method and proposed a fourth order multipoint iterative scheme for solving equations. Math. Comput. 20, 434--437 (1966; Zbl 0229.65049)]. Since then the Newton-Jarratt method has been widely studied for nonlinear equations, see \textit{J. Argyros} [J. Appl. Math. Comput. 28, No.~1--2, 15--28 (2008; Zbl 1159.65055)]. Further, \textit{J. Kou} and \textit{Y. Li} [Appl. Math. Comput. 189, No.~2, 1816--1821 (2007; Zbl 1122.65338)] have also proposed an improvement of the Jarratt method wherein the local order of convergence is improved from four for Jarratt method to six for the new method. The authors have not established a better accuracy in the present paper as compared to that of Kou and Li [loc. cit.].