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Cubo (Temuco)

versión On-line ISSN 0719-0646

Cubo vol.12 no.1 Temuco  2010

http://dx.doi.org/10.4067/S0719-06462010000100013 

CUBO A Mathematical Journal Vol.12, N° 01, (149-159). March 2010

 

An Improved Convergence and Complexity Analysis for the Interpolatory Newton Method


Ioannis K. Argyros

Cameron University, Department of Mathematical Sciences, Lawton, OK 73505, USA email : iargyros@cameron.edu


ABSTRACT

We provide an improved compared to local convergence analysis and complexity for the interpolatory Newton method for solving equations in a Banach space setting. The results are obtained using more precise error bounds than before and the same hypotheses/computational cost.

Key words and phrases: Newton's method, local convergence, Banach space, interpolatory Newton method, complexity, radius of convergence.


RESUMEN

Nosotros entregamos aquí un análisis de convergencia local y complejidad para el método de interpolación de Newton para resolver ecuaciones en espacios de Banach. Los resultados mejoran los de e son obtenidos usando mas precisas cotas de error y las mismas hipotesis y costo computacional.

Math. Subj. Class.: 65G99, 65H10, 65B05, 47H17, 49M15.


References

[1] Argyros, I.K., A unifying local-semilocal convergence analysis and applications for twopoint Newton-like methods in Banach space, J. Math. Anal. Applic., 298 (2004), 374-397.         [ Links ]

[2] Argyros, I.K., Approximate Solution of Operator Equations with Applications, World Scientific Publ. Comp., River Edge, New Jersey, 2005.         [ Links ]

[3] Argyros, I.K., An improved convergence and complexity analysis of Newton's method for solving equations, (to appear)         [ Links ].

[4] Kantorovich, L.V. and Akilov, G.P., Functional Analysis in Normed Spaces, Moscow, 1959.         [ Links ]

[5] Ortega, J.M. and Rheinboldt, W.C., Iterative Solution of Nonlinear Equations in Several Variables, Academic Press, New York, 1970.         [ Links ]

[6] Traub, J.F. and Wozniakowski, H., Strict lower and upper bounds on iterative computational complexity . In Analytic Computational Complexity, J.F. Traube, Ed., Academic Press, New York, 1976, pp. 15-34.         [ Links ]

[7] Traub, J.F. and Wozniakowski, H., Convergence and complexity of Newton iteration for operator equations, J. Assoc. Comput. Machinery, 26, No. 2 (1979), 250-258        [ Links ]

Received: October, 2008. Revised: January, 2009.

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