Extended Semi-Local Convergence of Newton's Method using the Center Lipschitz Condition and the Restricted Convergence Domain
Öz
The objective of this study is to extend the usage of Newton's method for Banach space valued operators. We use our new idea of restricted convergence domain in combination with the center Lipschitz hypothesis on the Frechet-derivatives where the center is not necessarily the initial point. This way our semi-local convergence analysis is tighter than in earlier works (since the new majorizing function is at least as tight as the ones used before) leading to weaker criteria, better error bounds more precise information on the solution. These improvements are obtained under the same computational effort.
Anahtar Kelimeler
Newton's method Banach space Center-Lipschitz condition Semi-local convergence
Kaynakça
- [1] I. K. Argyros, S. Hilout, Weaker conditions for the convergence of Newton’s method, J. Complexity, AMS, 28 (2012), 364–387.
- [2] I. K. Argyros, S. Hilout, On the quadratic convergence of Newton’s method under center-Lipschitz but not necessarily Lipschitz hypotheses, Math. Slovaca, 63 (2013), 621-638.
- [3] I. K. Argyros, A. A. Magrenan, Iterative Methods and Their Dynamics with Applications, CRC Press, New York, 2017.
- [4] H. T. Davis, Introduction to Nonlinear Differential and Integral Equations, Dover Pub., New York, 1992.
- [5] J. A. Ezquerro, D. Gonzalez, M. A. Hernandez, Majorizing sequences for Newton’s method from initial value problems, J. Comput. Appl. Math., 236 (2012), 2216–2238.
- [6] J. A. Ezquerro, M. A. Hernandez, Majorizing sequences for nonlinear Fredholdm-Hammerstein integral equations, Stud. Appl. Math., (2017), https://doi.org/10.1111/sapm.12200.
- [7] J. M. Gutierrez, A. A. Magrenan, N. Romero, On the semilocal convergence of Newton-Kantorovich method under center-Lipschitz conditions, Appl. Math. Comput., 221 (2013), 79–88.
- [8] Kantorovich, L.V., Akilov, G.P., Functional Analysis, Pergamon Press, Oxford, 1982.
- [9] L. B. Rall, Computational Solution of Nonlinear Operator equations, Robert E. Kreger Publishing Company, Michigan, 1979.
- [10] T. Yamamoto, Historical developments in convergence analysis for Newton’s and Newton-like methods, J. Comput. Appl. Math., 124 (2000), 1–23.
Öz
Kaynakça
- [1] I. K. Argyros, S. Hilout, Weaker conditions for the convergence of Newton’s method, J. Complexity, AMS, 28 (2012), 364–387.
- [2] I. K. Argyros, S. Hilout, On the quadratic convergence of Newton’s method under center-Lipschitz but not necessarily Lipschitz hypotheses, Math. Slovaca, 63 (2013), 621-638.
- [3] I. K. Argyros, A. A. Magrenan, Iterative Methods and Their Dynamics with Applications, CRC Press, New York, 2017.
- [4] H. T. Davis, Introduction to Nonlinear Differential and Integral Equations, Dover Pub., New York, 1992.
- [5] J. A. Ezquerro, D. Gonzalez, M. A. Hernandez, Majorizing sequences for Newton’s method from initial value problems, J. Comput. Appl. Math., 236 (2012), 2216–2238.
- [6] J. A. Ezquerro, M. A. Hernandez, Majorizing sequences for nonlinear Fredholdm-Hammerstein integral equations, Stud. Appl. Math., (2017), https://doi.org/10.1111/sapm.12200.
- [7] J. M. Gutierrez, A. A. Magrenan, N. Romero, On the semilocal convergence of Newton-Kantorovich method under center-Lipschitz conditions, Appl. Math. Comput., 221 (2013), 79–88.
- [8] Kantorovich, L.V., Akilov, G.P., Functional Analysis, Pergamon Press, Oxford, 1982.
- [9] L. B. Rall, Computational Solution of Nonlinear Operator equations, Robert E. Kreger Publishing Company, Michigan, 1979.
- [10] T. Yamamoto, Historical developments in convergence analysis for Newton’s and Newton-like methods, J. Comput. Appl. Math., 124 (2000), 1–23.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Matematik |
| Bölüm | Makaleler |
| Yazarlar | |
| Yayımlanma Tarihi | 17 Haziran 2019 |
| Gönderilme Tarihi | 27 Aralık 2018 |
| Kabul Tarihi | 4 Şubat 2019 |
| Yayımlandığı Sayı | Yıl 2019 Cilt: 2 Sayı: 1 |
Kaynak Göster
