Expanding the Applicability of a Third Order Newton-Type Method Free of Bilinear Operators

Abstract

This paper is devoted to the semilocal convergence, using centered hypotheses, of a third order Newton-type method in a Banach space setting. The method is free of bilinear operators and then interesting for the solution of systems of equations. Without imposing any type of Fréchet differentiability on the operator, a variant using divided differences is also analyzed. A variant of the method using only divided differences is also presented.

Keywords

• Newton type methods
• third order
• semilocal convergence
• centered hypotheses
• divided differences