Higher order Jarratt-like iterations for solving systems of nonlinear equations.

• The main advantage of the proposed methods is that they work well for any value of parameter "a" in the first stage of iterations, while the existing Jarratt-like methods work only for some a=2/3, 1/2. • To develop new methods with the highest possible order of convergence which requires the smallest possible evaluation of the function F and its derivatives and matrix inversions. • To extend the domain of applicability of existing methods. • From numerical results, clearly show that proposed method with the selected parameters are faster than other cases. In this article, we propose a new family of methods, such as Jarratt, with the fifth and sixth order. This includes some popular methods as special cases. We propose four different selection for parameter matrix T k. The main advantage of the proposed methods is that they work well for any value of parameter " a " in the first stage of iterations, while the existing methods work only for some a (2 / 3 or 1 / 2). Thus, we extend essentially the domain of applicability of the original ones. Based on the computational efficiency analysis, we also made a selection of some high-efficiency ones among the families. [ABSTRACT FROM AUTHOR]