José Luis Díaz Barrero

Note on the efficiency of some iterative methods for solving nonlinear equations

The efficiency of algorithms for solving nonlinear equations is a measure of comparison between different iterative methods. In the case of scalar equations two parameters are considered as it is well-known, but frequently in recent literature inaccurate generalizations combining these parameters are used when solving systems of nonlinear equations. Our goal in this paper is to clarify the concept of the efficiency in the multi-dimensional case. To do it we present a detailed definition of the computational efficiency. The relation between the efficiency parameters in scalar and vectorial cases is analyzed in detail and tested in two numerical examples.