Abstract

A generalization of the variants of Newton-s method based on interpolation rules of quadrature is obtained, in order to solve systems of nonlinear equations. Under certain conditions, convergence order is proved to be 2d C 1, where d is the order of the partial derivatives needed to be zero in the solution. Moreover, different numerical tests confirm the theoretical results and allow us to compare these variants with Newton-s classical method, whose convergence order is d C 1 under the same conditions. 2009 Elsevier B.V. All rights reserved.

Keywords

Nonlinear systems Newton-s method Fixed point iteration Convergence order

Referencia

A. Cordero, J.R. Torregrosa. On interpolation variants of Newton-s method for functions of several variables. Journal of Computational and Applied Mathematics 234 (2010) 34-43.