A unifying local-semilocal convergence analysis and applications for two-point Newton-like methods in Banach space

Journal of Mathematical Analysis and Applications

Volumn 298, Issue 2, 2004, Pages 374-397

  Argyros, Ioannis K ^a  

^a CAMERON UNIVERSITY   (United States)

Author keywords

Banach lemma on invertible operators; Banach space; Fr chet derivative; Majorizing sequence; Newton Kantorovich method hypothesis; Newton like method; Radius of convergence

Indexed keywords

EID: 10144254426     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jmaa.2004.04.008     Document Type: Article

References (26)

1. Allgower F.L. Böhmer K. Potra F.A. Rheinboldt W.C. A mesh independence principle for operator equations and their discretizations SIAM J. Numer. Anal. 23 1986 160-169
2. Appel J. DePascale E. Zabrejko P.P. On the application of the Newton-Kantorovich method to nonlinear integral equations of Uryson type Numer. Funct. Anal. Optim. 12 1991 271-283
3. Argyros I.K. Improving the rate of convergence of Newton methods on Banach spaces with a convergence structure and applications Appl. Math. Lett. 10 1977 21-28
4. Argyros I.K. Advances in the Efficiency of Computational Methods and Applications 2000 World Scientific River Edge, NJ
5. Argyros I.K. On the radius of convergence of Newton's method Internat. J. Comput. Math. 77 2001 389-400
6. Argyros I.K. A Newton-Kantorovich theorem for equations involving m-Fréchet-differentiable operators and applications in radiative transfer J. Comput. Appl. Math. 131 2001 149-159
7. Argyros I.K. Szidarovszky F. Convergence of general iteration schemes J. Math. Anal. Appl. 168 1992 42-52
8. Argyros I.K. Szidarovszky F. The Theory and Applications of Iteration Methods 1993 CRC Press Boca Raton, FL
9. Brown P.N. A local convergence theory for combined inexact-Newton/finite-difference projection methods SIAM J. Numer. Anal. 24 1987 407-434
10. Cǎtinas E. On some iterative methods for solving nonlinear equations Rev. Anal. Numér. Théor. Approx. 23 1994 47-53
11. Chen X. Yamamoto T. Convergence domains of certain iterative methods for solving nonlinear equations Numer. Funct. Anal. Optim. 10 1989 37-48
12. Dennis J.E. Toward a unified convergence theory for Newton-like methods In: Rall L.B. (Eds.) Nonlinear Functional Analysis and Applications 1971 425-472 Academic Press New York
13. Deuflhard P. Heindl G. Affine invariant convergence theorems for Newton's method and extensions to related methods SIAM J. Numer. Anal. 16 1979 1-10
14. Deuflhard P. Potra F.A. Asymptotic mesh independence of Newton-Galerkin methods via a refined Mysovskii theorem SIAM J. Numer. Anal. 29 1992 1395-1412
15. Gutiérrez J.M. Hernandez M.A. Salanova M.A. Accessibility of solutions by Newton's method Internat. J. Comput. Math. 57 1995 239-247
16. Kantorovich L.V. Akilov G.P. Functional Analysis 1982 Pergamon Oxford
17. Potra F.A. On an iterative algorithm of order 1.839... for solving nonlinear equations Numer. Funct. Anal. Optim. 7 1984-85 75-106
18. Potra F.A. Ptǎk V. Sharp error bounds for Newton's process Numer. Math. 34 1980 67-72
19. Rheinboldt W.C. An adaptive continuation process for solving systems of nonlinear equations Banach Center Publ. 3 1977 129-142
20. Schmidt J.W. Schwetlick H. Ableitungsfreie Verfahren mit hohere Konvergenzgeschwindigkeit Computing 3 1968 215-226
21. Schmidt J.W. Leonhardt H. Eingrenzung von Losungen mit der Regula Falsi Computing 6 1970 318-329
22. Schmidt J.W. Untere Fehlerschranken fur Regula-Falsi Verhafren Period. Math. Hungar. 9 1978 241-247
23. Uko L.U. Adeyeye J.O. Generalized Newton-iterative methods for nonlinear operator equations Nonlinear Studies 8 2001 465-477
24. Yamamoto T. A convergence theorem for Newton-like methods in Banach spaces Numer. Math. 51 1987 545-557
25. Ypma T.J. Local convergence of inexact Newton methods SIAM J. Numer. Anal. 21 1984 583-590
26. Zabrejko P.P. Nguen D.F. The majorant method in the theory of Newton-Kantorovich approximations and the Ptǎk error estimates Numer. Funct. Anal. Optim. 9 1987 671-684