An excellent numerical technique for multiple roots

Abstract

In recent times, some optimal eighth order iterative methods for computing multiple zeros of nonlinear functions have been appeared in literature. Different from these existing optimal methods, here we propose a new eighth order iterative method for multiple zeros. With four evaluations per iteration, the method satisfies the criterion of attaining optimal convergence of eighth order. Accuracy and computational efficiency are demonstrated by implementing the algorithm on different numerical problems. Moreover, the obtained results show its good convergence compared to existing optimal eighth order techniques. Besides, it also challenges the accuracy of existing methods which is the main advantage.