A generalization of Müller’s iteration method based on standard information

For finding a root of a function f, Müler’s method is a root-finding algorithm using three values of f in every step. The natural values available are values of f and values of its first number of derivatives, called standard information. Based on standard information, we construct an iteration method with maximal order of convergence. It is a natural generalization of Müller’s iteration method. This work was partially supported by National Natural Science Foundation of China (Grant No. 10471128), NSFC (Grant No. 10731060).