Abstract

Some variants of Newton-s method are developed in this work in order to solve nonlinear equations depending on one variable, based in rules of quadrature of 5th order. We prove the third or fifth order of convergence of these methods, depending on the behaviour of the second derivative. Moreover, different numeric tests confirm theoretic results and allow us to compare these variants with Newton-s classical method.

Keywords

Newton-s method Fixed point iteration Convergence order

Referencia

A.Cordero, J.R. Torregrosa (2006): Some variants of Newton-s method. Proceedings of the International Conference on Computational and Mathematical Methods in Science and Engineering, CMMSE 2006. Madrid, 21-25 September 2006, pp. 234-244