On a third‐order Newton‐type method free of bilinear operators

Abstract

Abstract This paper is devoted to the study of a third‐order Newton‐type method. The method is free of bilinear operators, which constitutes the main limitation of the classical third‐order iterative schemes. First, a global convergence theorem in the real case is presented. Second, a semilocal convergence theorem and some examples are analyzed, including quadratic equations and integral equations. Finally, an approximation using divided differences is proposed and used for the approximation of boundary‐value problems. Copyright © 2009 John Wiley & Sons, Ltd.