Extended Comparative Study between Newton’s and Steffensen-like Methods with Applications

Abstract

Comparisons between Newton’s and Steffensen-like methods are given for solving systems of equations as well as Banach space valued equations. Our idea of the restricted convergence domain is used to compare the sufficient convergence criteria of these methods under the same conditions as in previous papers. It turns out that the following advantages are shown: enlarged convergence domain; tighter error estimates and a more precise information on the location of the solution. Advantages are obtained under the same or at least as tight Lipschitz constants, which are specializations of earlier ones. Hence, the applicability of these methods is extended. Numerical experiments complete this study.

Keywords

• semi-local convergence
• Banach space
• Steffensen-like method
• Newton’s method