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  • P-ISSN1226-0657
  • E-ISSN2287-6081
  • KCI

ISSN : 1226-0657

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Vol.17 No.4

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ON THE SEMILOCAL CONVERGENCE OF THE GAUSS-NEWTON METHOD USING RECURRENT FUNCTIONS

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
2010, v.17 no.4, pp.307-319
Argyros, Ioannis K.
Hilout, Said
Argyros,, I. K. , & Hilout,, S. (2010). ON THE SEMILOCAL CONVERGENCE OF THE GAUSS-NEWTON METHOD USING RECURRENT FUNCTIONS. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 17(4), 307-319.

Abstract

We provide a new semilocal convergence analysis of the Gauss-Newton method (GNM) for solving nonlinear equation in the Euclidean space. Using our new idea of recurrent functions, and a combination of center-Lipschitz, Lipschitz conditions, we provide under the same or weaker hypotheses than before [7]-[13], a tighter convergence analysis. The results can be extented in case outer or generalized inverses are used. Numerical examples are also provided to show that our results apply, where others fail [7]-[13].

keywords
Gauss-Newton method, semilocal convergence, Frechet-derivative, More-Penrose pseudo-inverse

Reference

1.

H占�u占�ler. (1986). . Numerische Mathematik, 48(1), 119-125. 10.1007/BF01389446.

2.

Hu, N.;Shen, W.;Li, C.. (2008). Kantorovich's type theorems for systems of equations with constant rank derivatives. Journal of Computational and Applied Mathematics, 219(1), 110-122. 10.1016/j.cam.2007.07.006.

3.

4.

Penrose. (1955). . Mathematical Proceedings of the Cambridge Philosophical Society, 51(03), 406-413. 10.1017/S0305004100030401.

5.

Nashed, M. Z.;Chen, X.. (1993). Convergence of Newton-like methods for singular operator equations using outer inverses. Numerische Mathematik, 66(2), 235-257. 10.1007/BF01385696.

6.

Deuflhard, P.;Heindl, G.. (1979). Affine Invariant Convergence Theorems for Newton's Method and Extensions to Related Methods. SIAM Journal on Numerical Analysis, 16(1), 1-10. 10.1137/0716001.

7.

(2007). . J. Comput. Math., 25, 231-242.

8.

9.

Argyros, I. K.. (2005). A convergence analysis of Newton-like methods for singular equations using outer or generalized inverses. Applicationes Mathematicae, 32(1), 37-49. 10.4064/am32-1-3.

10.

(2005). . Adv. Nonlinear Var. Inequal., 8, 93-99.

11.

Argyros, I.K.. (2009). On the semilocal convergence of inexact Newton methods in Banach spaces. Journal of Computational and Applied Mathematics, 228(1), 434-443. 10.1016/j.cam.2008.10.005.

12.

Argyros, I.K.. (2004). On the Newton-Kantorovich hypothesis for solving equations. Journal of Computational and Applied Mathematics, 169(2), 315-332. 10.1016/j.cam.2004.01.029.

13.

(1999). . J. Comput. Anal. Appl., 1, 87-104.

14.

BENISRAEL. (1966). . Journal of Mathematical Analysis and Applications, 15(2), 243-252. 10.1016/0022-247X(66)90115-6.

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics

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