JOURNAL BROWSE
Search
Advanced SearchSearch Tips
ON A LOCAL CHARACTERIZATION OF SOME NEWTON-LIKE METHODS OF R-ORDER AT LEAST THREE UNDER WEAK CONDITIONS IN BANACH SPACES
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
ON A LOCAL CHARACTERIZATION OF SOME NEWTON-LIKE METHODS OF R-ORDER AT LEAST THREE UNDER WEAK CONDITIONS IN BANACH SPACES
Argyros, Ioannis K.; George, Santhosh;
  PDF(new window)
 Abstract
We present a local convergence analysis of some Newton-like methods of R-order at least three in order to approximate a solution of a nonlinear equation in a Banach space. Our sufficient convergence conditions involve only hypotheses on the first and second -derivative of the operator involved. These conditions are weaker that the corresponding ones given by Hernandez, Romero [10] and others [1], [4]-[9] requiring hypotheses up to the third derivative. Numerical examples are also provided in this study.
 Keywords
Newton-like methods;R-order of convergence;Banach space;local convergence;-derivative;
 Language
English
 Cited by
 References
1.
S. Amat, M. A. Hernandez, and N. Romero, A modified Chebyshev's iterative method with at least sixth order of convergence, Appl. Math. Comput. 206, (2008), no. 1, 164-174. crossref(new window)

2.
I. K. Argyros, Convergence and Application of Newton-type Iterations, Springer, 2008.

3.
I. K. Argyros and S. Hilout, A convergence analysis for directional two-step Newton methods, Numer. Algor. 55 (2010), 503-528. crossref(new window)

4.
V. Candela and A. Marquina, Recurrence relations for rational cubic methods I: The Halley method, Computing 44 (1990), 169-184. crossref(new window)

5.
V. Candela and A. Marquina, Recurrence relations for rational cubic methods II: The Chebyshev method, Computing 45 (1990), no. 4, 355-367. crossref(new window)

6.
J. A. Ezquerro and M. A. Hernandez, Recurrence relations for Chebyshev-type methods, Appl. Math. Optim. 41 (2000), no. 2, 227-236. crossref(new window)

7.
J. A. Ezquerro and M.A. Hernandez, New iterations of R-order four with reduced computational cost., BIT Numer. Math. 49 (2009), 325-342. crossref(new window)

8.
J. A. Ezquerro and M. A. Hernandez, On the R-order of the Halley method, J. Math. Anal. Appl. 303 (2005), 591-601. crossref(new window)

9.
W. Gander, On Halley's iteration method, Amer. Math. Monthly 92 (1985), 131-134. crossref(new window)

10.
M. A. Hernandez and N. Romero, On a characterization of some Newton-like methods of R-order at least three, J. Comput. Appl. Math. 183 (2005), 53-66. crossref(new window)

11.
L. V. Kantorovich and G. P. Akilov, Functional Analysis, Pergamon Press, Oxford, 1982.

12.
W. C. Rheinboldt, An adaptive continuation process for solving systems of nonlinear equations, In: Mathematical models and numerical methods (A. N. Tikhonov et al. eds.) pub. 3, (19), 129-142 Banach Center, Warsaw Poland.

13.
J. F. Traub, Iterative methods for the solution of equations, Prentice Hall Englewood Cliffs, New Jersey, USA, 1964.