REFERENCES
- F. Cianciaruso and E. De Pascale ( 2003 ). Newton–Kantorovich approximations the derivative is Hölderian: Old and new results . Numer. Funct. Anal. Optimss. 24 ( 7 & 8 ): 713 – 723 .
- N.T. Demidovich , P.P. Zabreiko , and Ju.V. Lysenko ( 1993 ). Some remarks on the Newton–Kantorovich method for nonlinear equations with Hölder continuous linearizations . Izv. Akad. Nauk Beloruss 3 : 322 – 326 [in Russian] .
- E. De Pascale and P.P. Zabreiko ( 1998 ). The convergence of the Newton–Kantorovich method under vertgeim conditions: A new improvement . Z. Anal. Anwend. 17 ( 2 ): 271 – 280 .
- L.V. Kantorovich and G.P. Akilov ( 1982 ). Functional Analysis [in Russian] . Nauka, Moscow , [Engl. Trans. : Pergamon Press , Oxford .]
- M.A. Krasnosel'skij , G.M. Vajnikko , P.P. Zabreiko , Ja.B. Rutitskij , and V.Ja. Stetsenko ( 1966/1972 ). Approximate Solutions of Operator Equations [in Russian] . Nauka, Moscow , [Engl. Trans. : Noordhoff , Groningen ].
- J.V. Lysenko ( 1994 ). Conditions for the convergence of the Newton–Kantorovich method for nonlinear equations with Hölder linearizations . Dokl. Akad. Nauk BSSR 38 : 20 – 24 [in Russian] . [CSA]
- J. Ortega and W. Rheinboldt ( 1970 ). Iterative solution of nonlinear equations in several variables . Academic Press , New York .
- B.A. Vertgeim ( 1956 ). On conditions for the applicability of Newton's method . Dokl. Akad. Nauk SSSR 110 : 719 – 722 [in Russian] . [CSA]
- B.A. Vertgeim ( 1957/1960 ). On some methods of the approximate solution of nonlinear functional equations in Banach spaces . Uspekhi Mat. Nauk 12 : 166 – 169 [in Russian]. [Engl. Trans. : Amer. Math. Soc. Transl. 16 ( 2 ): 378 – 382 .] [CSA]
- T. Yamamoto ( 2000 ). Historical developments in convergence analysis for Newton's and Newton-like methods . J. Comput. Appl. Math. 124 : 1 – 23 . [CSA] [CROSSREF]