Inexact Newton’s method for generalized operator equations in Banach spaces

• Autorzy: Singh V. K.

Identyfikatory

DOI

10.17512/jamcm.2018.4.09

• Języki publikacji: EN

Abstrakty

EN

In the present paper, we introduce a new inexact Newton-like algorithm for solving the generalized operator equations containing non differentiable operators in Banach space setting and discuss its semilocal convergence analysis under the weak Lipschitz condition with larger convergence domain and tighter error bounds. The main result of this paper is the significant improvement over the Newton’s method as well as the inexact Newton method.

Słowa kluczowe

EN

nonlinear operator equation; Fréchet derivative; Newton’s method; inexact; Newton method

PL

pochodna Frécheta; metoda Newtona; niedokładna metoda Newtona

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2018
• Tom: Vol. 17, nr 4
• Strony: 85--97
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Singh V. K.

• Department of Science and Humanities Government Polytechnic Korea Chhattishgarh, India-497335

Bibliografia

• [1] Kantorovich, L.V. (1948). On Newton’s method for functional equations. Doklady Akad. Nauk SSSR (N.S.), 59, 1237-1240 (Russian).
• [2] Kantorovich, L.V., & Akilov, G.P. (1982). Functional Analysis, Oxford: Pergamon Press.
• [3] Argyros, I.K., Khattri, S.K., & Hilout, S. (2013). Expanding the applicability of Inexact Newton Methods under Smale’s (a; g)-theory. Appl. Maths. Comput., 224, 24-237.
• [4] Morini, B. (1999). Convergence behaviour of inexact Newton methods. Math. Comput., 68, 1605-1613.
• [5] Li, C., & Shen, W.P. (2008). Local convergence of inexact methods under the H¨older condition. J. Comput. Appl. Math., 222, 544-560.
• [6] Shen, W.P., & Li, C. (2009). Kantorovich-type convergence criterion for inexact Newton methods. Appl. Numer. Math., 59, 1599-1611.
• [7] Shen, W.P., & Li, C. (2010). Smale’s a-theory for inexact Newton methods under the g-condition. J. Math. Anal. Appl., 369, 29-42.
• [8] Xu, X., Xiao, Y., & Liu, T. (2012). Semilocal convergence analysis for inexact Newton method under weak condition. Abstract Appl. Anal., art. ID 982925, 13 pp.
• [9] Dembo, R.S., Eisenstat, S.C., & Steihaug, T. (1982). Inexact Newton methods. Siam J. Numer. Anal., 19, 400-408.
• [10] Argyros, I.K., & Santosh, G. (2017). Exposnding the applicability of inexact Newton methods using restricted Convergence domain. Applicationes Mathematicae, 44(1), 123-133.
• [11] Wang, X.H. (1999). Convergence of Newton’s method and inverse function theorem in Banach space. Math. Comput., 68, 169-186.
• [12] Tapia, R.A. (1971). The Kantorovich theorem for Newton’s method. Amer. Math. Mon., 78, 389-392.

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).