Three new optimal fourth-order iterative methods to solve nonlinear equations
Summary: We present new modifications to Newton's method for solving nonlinear equations. The analysis of convergence shows that these methods have fourth-order convergence. Each of the three methods uses three functional evaluations. Thus, according to Kung-Traub's conjecture (cf. [\textit{H. T. Kung} and \textit{J. F. Traub}, J. Assoc. Comput. Mach. 21, 643--651 (1974; Zbl 0289.65023)]), these are optimal methods. With the previous ideas, we extend the analysis to functions with multiple roots. Several numerical examples are given to illustrate that the presented methods have better performance compared with Newton's classical method and other methods of fourth-order convergence recently published.
scientific article; zbMATH DE number 6171670