LOCAL CONVERGENCE ANALYSIS OF INEXACT NEWTON-LIKE METHODS
-
1677
Downloads
-
2747
Views
Authors
IOANNIS K. ARGYROS
- Cameron university, Department of Mathematics Sciences, Lawton, OK 73505, USA..
SAID HILOUT
- Poitiers university, Laboratoire de Mathématiques et Applications, Bd. Pierre et Marie Curie, Téléport 2, B.P. 30179, 86962 Futuroscope Chasseneuil Cedex, France..
Abstract
We provide a local convergence analysis of inexact Newton–like
methods in a Banach space setting under flexible majorant conditions. By
introducing center–Lipschitz–type condition, we provide (under the same computational
cost) a convergence analysis with the following advantages over earlier
work [9]: finer error bounds on the distances involved, and a larger radius
of convergence.
Special cases and applications are also provided in this study.
Share and Cite
ISRP Style
IOANNIS K. ARGYROS, SAID HILOUT, LOCAL CONVERGENCE ANALYSIS OF INEXACT NEWTON-LIKE METHODS, Journal of Nonlinear Sciences and Applications, 2 (2009), no. 1, 11-18
AMA Style
ARGYROS IOANNIS K., HILOUT SAID, LOCAL CONVERGENCE ANALYSIS OF INEXACT NEWTON-LIKE METHODS. J. Nonlinear Sci. Appl. (2009); 2(1):11-18
Chicago/Turabian Style
ARGYROS , IOANNIS K., HILOUT, SAID. "LOCAL CONVERGENCE ANALYSIS OF INEXACT NEWTON-LIKE METHODS." Journal of Nonlinear Sciences and Applications, 2, no. 1 (2009): 11-18
Keywords
- Inexact Newton–like method
- Banach space
- Majorant conditions
- Local convergence.
MSC
- 65H10
- 65G99
- 90C30
- 49M15
- 47J20
References
-
[1]
I. K. Argyros, Relation between forcing sequences and inexact Newton iterates in Banach space, Computing, 63 (1999), 134–144.
-
[2]
I. K. Argyros, Forcing sequences and inexact Newton iterates in Banach space, Appl. Math. Lett. , 13 (2000), 69–75.
-
[3]
I. K. Argyros, 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.
-
[4]
I. K. Argyros, Computational theory of iterative methods, Series: Studies in Computational Mathematics, 15, Editors: C.K. Chui and L. Wuytack, Elsevier Publ. Co., New York, USA (2007)
-
[5]
I. K. Argyros, Convergence and applications of Newton–type iterations, Springer–Verlag Publ., New York (2008)
-
[6]
I. K. Argyros, On the semilocal convergence of inexact Newton methods in Banach spaces, J. Comput. Appl. Math. in press, (doi:10.1016/j.cam.2008.10.005. ),
-
[7]
J. Chen, W. Li , Convergence behaviour of inexact Newton methods under weak Lipschitz condition, J. Comput. Appl. Math. , 191 (2006), 143–164.
-
[8]
J. F. Dennis, Toward a unified convergence theory for Newton–like methods, in Nonlinear Functional Analysis and Applications (L.B. Rall, ed.), Academic Press, New York, (1971), 425–472.
-
[9]
O. P. Ferreira, M. L. N. Goncalves, Local convergence analysis of inexact Newton–like methods under majorant condition, preprint, http://arxiv.org/abs/0807.3903?context=math.OC., (document),
-
[10]
X. Guo, On semilocal convergence of inexact Newton methods, J. Comput. Math., 25 (2007), 231–242.
-
[11]
Z. A. Huang, Convergence of inexact Newton method, J. Zhejiang Univ. Sci. Ed., 30 (2003), 393–396.
-
[12]
L. V. Kantorovich, G. P. Akilov, Functional Analysis, Pergamon Press, Oxford (1982)
-
[13]
B. Morini, Convergence behaviour of inexact Newton methods, Math. Comp. , 68 (1999), 1605–1613.
-
[14]
F. A. Potra , Sharp error bounds for a class of Newton–like methods, Libertas Mathematica. , 5 (1985), 71–84.
-
[15]
X. H. Wang, C. Li , Convergence of Newton’s method and uniqueness of the solution of equations in Banach spaces, II, Acta Math. Sin. (Engl. Ser.) , 19 (2003), 405–412.