On optimal multipoint methods for solving nonlinear equations


Miodrag S. Petković




A general class of three-point iterative methods for solving nonlinear equations is constructed. Its order of convergence reaches \emph{eight} with only \emph{four} function evaluations per iteration, which means that the proposed methods possess as high as possible computational efficiency in the sense of the Kung-Traub hypothesis (1974). Numerical examples are included to demonstrate a spectacular convergence speed with only few function evaluations.