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http://dx.doi.org/10.7468/jksmeb.2011.18.3.219

ON THE RADIUS OF CONVERGENCE OF SOME NEWTON-TYPE METHODS IN BANACH SPACES

Argyros, Ioannis K. (Cameron university, Department of Mathematics Sciences)
Hilout, Said (Poitiers university, Laboratoire de Mathematiques et Applications)

Publication Information

The Pure and Applied Mathematics / v.18, no.3, 2011 , pp. 219-230 More about this Journal

Abstract

We determine the radius of convergence for some Newton{type methods (NTM) for approximating a locally unique solution of an equation in a Banach space setting. A comparison is given between the radii of (NTM) and Newton's method (NM). Numerical examples further validating the theoretical results are also provided in this study.

Keywords

Newton's method; Newton-type method; Banach space; local convergence; radius of convergence; Lipschitz-H $\ddot{o}$ lder continuity;

Citations & Related Records

Reference

1	Traub, J.F. & Wozniakowsi, H.: Convergence and complexity of Newton iteration for operator equations. J. Assoc. Comput. Mach. 26 (1979), 250-258. DOI ScienceOn
2	Hernandez, M.A. & Romero, N.: On a characterization of some Newton-like methods of R-order at least three. J. Comput. Appl. Math. 183 (2005), 53-66. DOI ScienceOn
3	Kantorovich, L.V. & Akilov, G.P.: Functional Analysis in normed spaces, Pergamon Press, Oxford, 1982.
4	Proinov, P.D.: General local convergence theory for a class of iterative processes and its applications to Newton's method. J. Complexity 25 (2009), 38-62. DOI ScienceOn
5	Rheinboldt, W.C.: An adaptative continuation process for solving systems of nonlinear equations. Polish Acad. of Sciences, Banach Ctr. Publ. 3 (1977), 129-142.
6	Argyros, I.K. & Hilout, S.: Efficient methods for solving equations and variational inequalities. Polimetrica Publisher, Milano, Italy, 2009.
7	Argyros, I.K.: On the radius of convergence of Newton's method. Intern. J. Comput. Math. 77 (2001), 389-400. DOI ScienceOn
8	Ezquerro, J.A., Hernandez, M.A. & Salanova, M.A.: A discretization scheme for some conservative problems. Proceedings of the 8th Inter. Congress on Comput. and Appl. Math., ICCAM-98 (Leuven), J. Comput. Appl. Math. 115 (2000), 181-192. DOI
9	Ezquerro, J.A., Hernandez, M.A. & Salanova, M.A.: A Newton-like method for solving some boundary value problems. Numer. Funct. Anal. Optimiz. 23 (2002), 791-805. DOI ScienceOn
10	Gupta, D.K. & Parhi, S.K.: A third order method for fixed points in Banach spaces. J. Math. Anal. Appl. 359 (2009), 642-652. DOI ScienceOn
11	Argyros, I.K.: A unifying local-semilocal convergence analysis and applications for two-point Newton-like methods in Banach space. J. Math. Anal. Appl. 298 (2004), 374-397. DOI ScienceOn
12	Argyros, I.K.: Convergence and applications of Newton-type iterations. Springer-Verlag, 2008, New York.