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A semilocal convergence analysis for directional Newton methods
Author(s):
Ioannis
K.
Argyros.
Journal:
Math. Comp.
80
(2011),
327-343.
MSC (2010):
Primary 65H05, 65H10;
Secondary 49M15
Posted:
July 8, 2010
MathSciNet review:
2728982
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Additional information
Abstract:
A semilocal convergence analysis for directional Newton methods in  -variables is provided in this study. Using weaker hypotheses than in the elegant related work by Y. Levin and A. Ben-Israel and introducing the center-Lipschitz condition we provide under the same computational cost as in Levin and Ben-Israel a semilocal convergence analysis with the following advantages: weaker convergence conditions; larger convergence domain; finer error estimates on the distances involved, and an at least as precise information on the location of the zero of the function. A numerical example where our results apply to solve an equation but not the ones in Levin and Ben-Israel is also provided in this study.
References:
-
- 1.
- I. K. Argyros, On the Newton-Kantorovich hypothesis for solving equations, J. Comput. Appl. Math., 169 (2004), 315-332. MR 2072881 (2005c:65047)
- 2.
- 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. MR 2086964
- 3.
- I. K. Argyros, Convergence and applications of Newton-type iterations, Springer-Verlag, 2008, New York. MR 2428779
- 4.
- A. Ben-Israel, Y. Levin, Maple programs for directional Newton methods, are available at ftp://rutcor.rutgers.edu/pub/bisrael/Newton-Dir.mws.
- 5.
- Y. Levin, A. Ben-Israel, Directional Newton methods in
 variables, Mathematics of Computation, A.M.S., 71 (2002), 251-262. MR 1862998 (2002h:65083) - 6.
- G. Lukács, The generalized inverse matrix and the surface-surface intersection problem. Theory and practice of geometric modeling (Blaubeuren, 1988), 167-185, Springer, Berlin, 1989. MR 1042329 (91f:65041)
- 7.
- J. M. Ortega, W. C. Rheinboldt, Iterative solution of nonlinear equations in several variables, Academic Press, New York, 1970. MR 0273810 (42:8686)
- 8.
- V. Pereyra, Iterative methods for solving nonlinear least square problems, SIAM J. Numer. Anal., 4 (1967), 27-36. MR 0216732 (35:7561)
- 9.
- B. T. Polyak, Introduction to optimization. Translated from the Russian. With a foreword by D.P. Bertsekas. Translations Series in Mathematics and Engineering. Optimization Software, Inc., Publications Division, New York, 1987. MR 1099605 (92b:49001)
- 10.
- A. Ralston, P. Rabinowitz, A first course in numerical analysis, 2nd Edition, McGraw-Hill, 1978. MR 0494814 (58:13599)
- 11.
- J. Stoer, K. Bulirsch, Introduction to numerical analysis, Springer-Verlag, 1980. MR 0557543 (83d:65002)
- 12.
- H. F. Walker, L. T. Watson, Least-change secant update methods, SIAM J. Numer. Anal., 27 (1990), 1227-1262. MR 1061128 (91g:65121)
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Additional Information:
Ioannis
K.
Argyros
Affiliation:
Department of Mathematics Sciences, Cameron University, Lawton, Oklahoma 73505
Email:
iargyros@cameron.edu
DOI:
10.1090/S0025-5718-2010-02398-1
PII:
S 0025-5718(2010)02398-1
Keywords:
Directional Newton method,
systems of equations,
Lipschitz/center-Lipschitz condition,
Newton–Kantorovich-type hypothesis
Received by editor(s):
May 5 2008
Received by editor(s) in revised form:
August 10, 2009
Posted:
July 8, 2010
Copyright of article:
Copyright
2010,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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