Semilocal convergence of a sixth order iterative method for quadratic equations.
- Amat, S. 1
- Hernández, M.A. 2
- Romero, N. 2
-
1
Universidad Politécnica de Cartagena
info
-
2
Universidad de La Rioja
info
ISSN: 0168-9274
Any de publicació: 2012
Volum: 62
Número: 7
Pàgines: 833-841
Tipus: Article
beta Ver similares en nube de resultadosAltres publicacions en: Applied Numerical Mathematics
Projectes relacionats
Resum
In this paper the modification of Chebyshev's iterative method constructed in Amat et al. (2008) [1] is revisited. The behavior of this method when considering quadratic nonlinear operators is analyzed. In this case, the iterative method has a competitive behavior due to its computational efficiency. Moreover, a new result of semilocal convergence assuming only a pointwise condition is obtained, improving the result given in Amat et al. (2008) [1]. The domain of uniqueness of the solution is also improved. The new technique used in the proof of these results allows us to achieve all these improvements. Finally, some theoretical and numerical applications for a quadratic system of equations are presented. © 2012 IMACS. Published by Elsevier B.V. All rights reserved.