JOURNAL BROWSE
Search
Advanced SearchSearch Tips
LOCAL CONVERGENCE OF THE GAUSS-NEWTON METHOD FOR INJECTIVE-OVERDETERMINED SYSTEMS
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
LOCAL CONVERGENCE OF THE GAUSS-NEWTON METHOD FOR INJECTIVE-OVERDETERMINED SYSTEMS
Amat, Sergio; Argyros, Ioannis Konstantinos; Magrenan, Angel Alberto;
  PDF(new window)
 Abstract
We present, under a weak majorant condition, a local convergence analysis for the Gauss-Newton method for injective-overdetermined systems of equations in a Hilbert space setting. Our results provide under the same information a larger radius of convergence and tighter error estimates on the distances involved than in earlier studies such us [10, 11, 13, 14, 18]. Special cases and numerical examples are also included in this study.
 Keywords
the Gauss-Newton method;Hilbert spaces;majorant condition;local convergence;radius of convergence;injective-overdetermined systems;
 Language
English
 Cited by
 References
1.
S. Amat, S. Busquier, and J. M. Gutierrez, Geometric constructions of iterative functions to solve nonlinear equations, J. Comput. Appl. Math. 157 (2003), no. 1, 197-205. crossref(new window)

2.
J. Appel, E. De Pascale, J. V. Lysenko, and P. P. Zabrejko, New results on Newton-Kantorovich approximations with applications to nonlinear integral equations, Numer. Funct. Anal. Optimiz. 18 (1997), no. 1-2, 1-17.

3.
I. K. Argyros, Computational Theory of Iterative Methods, Studies in Computational Mathematics, 15, Editors: K. Chui and L. Wuytach. Elsevier, 2007.

4.
I. K. Argyros, Concerning the semilocal convergence of Newton's method and convex majorants, Rend. Circ. Mat. Palermo (2) 57 (2008), no. 3, 331-341. crossref(new window)

5.
I. K. Argyros, Concerning the convergence of Newton's method and quadratic majorants, J. Appl. Math. Comput. 29 (2009), no. 1-2, 391-400. crossref(new window)

6.
I. K. Argyros, A semilocal convergence analysis for directional Newton methods, Math. Comp. 80 (2011), no. 273, 327-343.

7.
I. K. Argyros and S. Hilout, Extending the applicability of the Gauss-Newton method under average Lipschitz-conditions, Numer. Algorithms 58 (2011), no. 1, 23-52. crossref(new window)

8.
I. K. Argyros and S. Hilout, Improved local convergence of Newton's method under weak majorant condition, J. Comput. Appl. Math. 236 (2012), no. 7, 1892-1902. crossref(new window)

9.
I. K. Argyros and S. Hilout, Computational Methods in Nonlinear Analysis, World Scientific Publ. Comp., New Jersey, 2013.

10.
O. P. Ferreira, Local convergence of Newton's method in Banach space from the viewpoint of the majorant principle, IMA J. Numer. Anal. 29 (2009), no. 3, 746-759. crossref(new window)

11.
O. P. Ferreira, Local convergence of Newton's method under majorant condition, J. Comput. Appl. Math. 235 (2011), no. 5, 1515-1522. crossref(new window)

12.
O. P. Ferreira, M. L. N. Goncalves, and P. R. Oliveira, Local convergence analysis of the Gauss-Newton method under a majorant condition, J. Complexity 27 (2011), no. 1. 111-125. crossref(new window)

13.
O. P. Ferreira and B. F. Svaiter, Kantorovich's majorants principle for Newton's method, Comput. Optim. Appl. 42 (2009), no. 2, 213-229. crossref(new window)

14.
M. L. N. Goncalves, Local convergence of the Gauss-Newton method for injective-overdetermined systems of equations under a majorant condition, Comput. Math. Appl. 66 (2013), no. 4, 490-499. crossref(new window)

15.
J. M. Gutierrez, M. A. Hernandez, and M. A. Salanova, Accessibility of solutions by Newton's method, Inter. J. Comput. Math. 57 (1995), no. 3-4, 239-247. crossref(new window)

16.
W. M. A. Haussler, Kantorovich-type convergence analysis for the Gauss-Newton method, Numer. Math. 48 (1986), no. 1, 119-125. crossref(new window)

17.
L. V. Kantorovich and G. P. Akilov, Functional Analysis in Normed Spaces, Pergamon Press, Oxford, 1964.

18.
C. Li and K. F. Ng, Majorizing functions and convergence of the Gauss-Newton method for convex composite optimization, SIAM J. Optim. 18 (2007), no. 2, 613-692. crossref(new window)

19.
A. A. Magrenan, Estudio de la dinamica del metodo de Newton amortiguado, PhD Thesis, Servicio de Publicaciones, Universidad de La Rioja, 2013.

20.
P. D. Proinov, General local convergence theory for a class of iterative processes and its applications to Newton's method, J. Complexity 25 (2009), no. 1, 38-62. crossref(new window)

21.
W. C. Rheinboldt, An adaptive continuation process for solving systems of nonlinear equations, Polish Academy of Science, Banach Ctr. Publ. 3 (1977), no. 1, 129-142.

22.
X. Wang, Convergence on Newton's method and inverse function theorem in Banach space, Math. Comput. 68 (1999), no. 225, 169-186. crossref(new window)