A class of computationally efficient numerical algorithms for locating multiple zeros

Abstract

In recent times, many iterative methods for computing multiple zeros of nonlinear functions have been appeared in literature. Different from these existing methods, here we propose a new class of methods with eighth order convergence for multiple zeros. With four evaluations per iteration, the methods satisfy the criterion of attaining optimal convergence of eighth order. Applicability is demonstrated on different examples that illustrates the computational efficiency of novel methods. Comparison of numerical results shows that the proposed techniques possess good convergence compared to existing optimal order techniques. Besides, the accuracy of existing techniques is also challenged which is the main advantage.