An improved Newton–Traub composition for solving systems of nonlinear equations

In this paper, we present a modified Newton–Traub composition with increasing order of convergence for solving systems of nonlinear equations. The idea is based on the recent development by Sharma et al. (2015). Analysis of convergence shows that the presented method has sixth order of convergence. Computational efficiency of the new method is considered and compared with some well-known existing methods. Numerical tests are performed on some problems of different nature, which confirm robust and efficient convergence behavior of the proposed method. Moreover, theoretical results concerning order of convergence and computational efficiency are verified in the numerical problems. The basins of attraction of existing methods and the presented method are given to demonstrate their performance.