Comparative study of eighth-order methods for finding simple roots of nonlinear equations

Abstract

Recently, there were many papers discussing the basins of attraction of various methods and ideas how to choose the parameters appearing in families of methods and weight functions used. Here, we collected many of the eighth-order schemes scattered in the literature and presented a quantitative comparison. We have used the average number of function evaluations per point, the CPU time, and the number of black points to compare the methods. Based on seven examples, we found that the best method based on the three criteria is SA8 due to Sharma and Arora.