A Family of Three-Point Methods of Ostrowski's Type for Solving Nonlinear Equations

[摘要] A class of three-point methods for solving nonlinear equations of eighth order is constructed. These methods are developed by combining two-point Ostrowski's fourth-order methods and amodified Newton's method in the third step, obtained by a suitable approximation of the firstderivative using the product of three weight functions. The proposed three-step methods haveorder eight costing only four function evaluations, which supports the Kung-Traub conjectureon the optimal order of convergence. Two numerical examples for various weight functions aregiven to demonstrate very fast convergence and high computational efficiency of the proposedmultipoint methods.

[学科分类] 应用数学