References

ON NEWTON'S METHOD DEFINED ON NOT NECESSARILY BOUNDED DOMAINS


[1] I. K. Argyros and R. U. Verma, Semilocal convergence theorems for a certain class of iterative procedures involving m-Fréchet differentiable operators, Math. Sci. Res. Hot-Line 4 (2000), 1-12.

[2] I. K. Argyros, Error bounds for Newton’s method under hypotheses on the m-th Fréchet derivative, Adv. Nonlinear Var. Inequal. 4 (2001), 23-33.

[3] I. K. Argyros, On the convergence of Newton-like methods based on m-Fréchet differentiable operators and applications in radiative transfer, J. Comput. Anal. Appl. 4 (2002), 141-154.

[4] 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.

[5] I. K. Argyros, Computational Theory of Iterative Methods, Series: Studies in Computational Mathematics, 15, Editors: C.K. Chui and L. Wuytack, Elsevier Publ. Co., New York, USA, 2007.

[6] I. K. Argyros, On a class of Newton-like methods for solving nonlinear equations, J. Comput. Appl. Math., in press, doi:10.1016/j.cam.2008.08.042.

[7] S. Chandrasekhar, Radiative Transfer, Dover Publ., New York, 1960.

[8] J. E. Dennis, Toward a Unified Convergence Theory for Newton-like Methods, in Nonlinear Functional Analysis and Applications (L. B. Rall, ed.), Academic Press, New York, (1971), 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. M. Gutiérrez, A new semilocal convergence theorem for Newton’s method, J. Comput. Appl. Math. 79 (1997), 131-145.

[11] Z. Huang, A note of Kantorovich theorem for Newton iteration, J. Comput. Appl. Math. 47 (1993), 211-217.

[12] L. V. Kantorovich and G. P. Akilov, Functional Analysis, Pergamon Press, Oxford, 1982.

[13] F. A. Potra, Sharp error bounds for a class of Newton-like methods, Libertas Mathematica 5 (1985), 71-84.

[14] T. Yamamoto, A convergence theorem for Newton-like methods in Banach spaces, Numer. Math. 51 (1987), 545-557.