Solving equations using Newton's method under weak conditions on Banach spaces with a convergence structure
DOI:
https://doi.org/10.33993/jnaat371-871Keywords:
Newton's method, Banach spaces with a convergence structure, semilocal convergence, Fréchet-derivative, majorant principle, fixed point, Newton-Kantorovich theorem/hypothesisAbstract
We provide new semilocal results for Newton's method on Banach spaces with a convergence structure. Using more precise majorizing sequence we show that, under weaker convergence conditions than before, we can obtain finer error bounds on the distances involved and a more precise information on the location of the solution.Downloads
References
Argyros, I. K., Newton methods on Banach spaces with on convergence structure and applications, computers and Mathematics with Applications, 40, 1, pp. 37-48, 2000, https://doi.org/10.1016/s0898-1221(00)00138-3 DOI: https://doi.org/10.1016/S0898-1221(00)00138-3
Argyros, I. K., Advances in the efficiency of computational methods and applications, World Scientific Publ. Co. River Edge, New Jersey, 2000, https://doi.org/10.1142/4448 DOI: https://doi.org/10.1142/4448
Argyros, I. K., An improved error analysis for Newton-like methods under generalized conditions, J. Comput. Appl. Math. 157, 1, pp. 169-185, 2003, https://doi.org/10.1016/s0377-0427(03)00390-x DOI: https://doi.org/10.1016/S0377-0427(03)00390-X
Kantorovich, L. V., and Akilov, G. P., Functional Analysis in normed spaces, Pergamon Press, Oxford, 1982. DOI: https://doi.org/10.1016/B978-0-08-023036-8.50010-2
Meyer, P. W., Newton's method in generalized Banach spaces, Numer. Funct. Anal. and Optimiz. 9, pp. 249-259, 1987, https://doi.org/10.1080/01630568708816234 DOI: https://doi.org/10.1080/01630568708816234
Meyer, P. W., A unifying theorem on Newton's method, Numer. Funct. Anal. and Optimiz., 13, (5 and 6), pp. 463-473, 1992, https://doi.org/10.1080/01630569208816492 DOI: https://doi.org/10.1080/01630569208816492
Vandergraft, J. A., Newton's method for convex operators in partially ordered spaces, SIAM J. Numer. Anal. 4, pp. 406-432, 1967, https://doi.org/10.1137/0704037 DOI: https://doi.org/10.1137/0704037
Yamamoto, J., A unified derivation of several error bounds for Newton's process, J. Comput. Appl. Math. 12 and 13, pp. 179-191, 1985, https://doi.org/10.1016/0377-0427(85)90015-9 DOI: https://doi.org/10.1016/0377-0427(85)90015-9
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2015 Journal of Numerical Analysis and Approximation Theory
This work is licensed under a Creative Commons Attribution 4.0 International License.
Open Access. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
