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

Abstract

The e ciency of algorithms for solving nonlinear equations is a measure of comparison between di erent 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 e ciency in the multi-dimensional case. To do it we present a detailed de nition of the computational e ciency. The relation between the e ciency parameters in scalar and vectorial cases is analyzed in detail and tested in two numerical examples