Improved generalized differentiability conditions for Newton-like methods

Journal of Complexity

Volumn 26, Issue 3, 2010, Pages 316-333

  Argyros, Ioannis K ^a   Hilout, Saïd ^b  

^a CAMERON UNIVERSITY   (United States)

^b UNIVERSITÉ DE POITIERS   (France)

Author keywords

Chandrasekhar nonlinear integral equation; Differential equation with Green's kernel; Majorizing sequence; Newton like method; Radiative transfer; Semilocal convergence

Indexed keywords

COMPUTATION THEORY; CONVERGENCE OF NUMERICAL METHODS; DIFFERENTIAL EQUATIONS; NEWTON-RAPHSON METHOD; NONLINEAR EQUATIONS; RADIATIVE TRANSFER;

COMPUTATIONAL COSTS; CONVERGENCE CONDITIONS; GENERALIZED DIFFERENTIABILITY; MAJORIZING SEQUENCES; NEWTON LIKE METHODS; NEWTON'S METHODS; NONLINEAR INTEGRAL EQUATIONS; SEMI-LOCAL CONVERGENCES;

INTEGRAL EQUATIONS;

EID: 77955712562     PISSN: 0885064X     EISSN: 10902708     Source Type: Journal    
DOI: 10.1016/j.jco.2009.12.001     Document Type: Article

References (20)

1. I.K. Argyros On the NewtonKantorovich hypothesis for solving equations J. Comput. Appl. Math. 169 2004 315 332
2. I.K. Argyros A unifying localsemilocal convergence analysis and applications for two-point Newton-like methods in Banach space J. Math. Anal. Appl. 298 2004 374 397
3. I.K. Argyros Computational Theory of Iterative Methods C.K. Chui, L. Wuytack, Series: Studies in Computational Mathematics vol. 15 2007 Elsevier Publ. Co. New York, USA
4. I.K. Argyros, and S. Hilout Efficient methods for solving equations and variational inequalities 2009 Polimetrica Publisher Milano, Italy
5. I.K. Argyros, and S. Hilout Aspects of the computational theory for certain iterative methods 2009 Polimetrica Publisher
6. I.K. Argyros, and S. Hilout On the weakening of the convergence of Newton's method using recurrent functions J. Complexity 25 2009 530 543
7. X. Chen, and T. Yamamoto Convergence domains of certain iterative methods for solving nonlinear equations Numer. Funct. Anal. Optim. 10 1989 37 48
8. J.E. Dennis Toward a unified convergence theory for Newton-like methods L.B. Rall, Nonlinear Functional Analysis and Applications 1971 Academic Press New York 425 472
9. P. Deuflhard, and G. Heindl Affine invariant convergence theorems for Newton's method and extensions to related methods SIAM J. Numer. Anal. 16 1979 1 10
10. J.A. Ezquerro, and M.A. Hernndez Generalized differentiability conditions for Newton's method IMA J. Numer. Anal. 22 2002 187 205
11. J.M. Gutirrez A new semilocal convergence theorem for Newton's method J. Comput. Appl. Math. 79 1997 131 145
12. Z. Huang A note of Kantorovich theorem for Newton iteration J. Comput. Appl. Math. 47 1993 211 217
13. L.V. Kantorovich, and G.P. Akilov Functional Analysis 1982 Pergamon Press Oxford
14. J.M. Ortega, and W.C. Rheinboldt Iterative Solution of Nonlinear Equations in Several Variables 1970 Academic Press New York
15. F.A. Potra Sharp error bounds for a class of Newton-like methods Libertas Math. 5 1985 71 84
16. P.D. Proinov General local convergence theory for a class of iterative processes and its applications to Newton's method J. Complexity 25 2009 38 62
17. P.D. Proinov New general convergence theory for iterative processes and its applications to NewtonKantorovich type theorems J. Complexity 26 2010 3 42
18. W.C. Rheinboldt A unified convergence theory for a class of iterative processes SIAM J. Numer. Anal. 5 1968 42 63
19. T. Yamamoto A convergence theorem for Newton-like methods in Banach spaces Numer. Math. 51 1987 545 557
20. P.P. Zabrejko, and D.F. Nguen The majorant method in the theory of NewtonKantorovich approximations and the Ptk error estimates Numer. Funct. Anal. Optim. 9 1987 671 684