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Volumn 24, Issue 7-8, 2003, Pages 713-723

Newton-Kantorovich approximations when the derivative is Hölderian: Old and new results

Author keywords

H lder continuous derivative; Newton Kantorovich approximations; Regions of convergence

Indexed keywords

BOUNDARY CONDITIONS; CONVERGENCE OF NUMERICAL METHODS; MATHEMATICAL OPERATORS; PROBLEM SOLVING; THEOREM PROVING;

EID: 0347603934     PISSN: 01630563     EISSN: None     Source Type: Journal    
DOI: 10.1081/NFA-120026367     Document Type: Article
Times cited : (29)

References (12)
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    • Appell, J., De Pascale, E., Lysenko, Ju. V., Zabreiko, P. P. (1997). New results on Newton-Kantorovich approximations with applications to nonlinear integral equations. Numer. Funct. Anal. Optim. 18(1&2):1-18.
    • (1997) Numer. Funct. Anal. Optim. , vol.18 , Issue.1-2 , pp. 1-18
    • Appell, J.1    De Pascale, E.2    Lysenko, Ju.V.3    Zabreiko, P.P.4
  • 2
    • 84892022813 scopus 로고    scopus 로고
    • The Newton-Kantorovich approximations for the nonlinear integro-differential equations of mixed type
    • (to appear)
    • Cianciaruso, F., De Pascale, E. (2002). The Newton-Kantorovich approximations for the nonlinear integro-differential equations of mixed type. Ric. Mat. LI fasc. 2 (to appear).
    • (2002) Ric. Mat. LI Fasc. , vol.2
    • Cianciaruso, F.1    De Pascale, E.2
  • 3
    • 0346751436 scopus 로고
    • Some remarks on the Newton-Kantorovich method for nonlinear equations with Hölder continuous linearizations
    • (in Russian)
    • Demidovich, N. T., Zabreiko, P. P., Lysenko, Ju. V. (1993). Some remarks on the Newton-Kantorovich method for nonlinear equations with Hölder continuous linearizations. Izv. Akad. Nauk. Beloruss 3:22-26. (in Russian).
    • (1993) Izv. Akad. Nauk. Beloruss , vol.3 , pp. 22-26
    • Demidovich, N.T.1    Zabreiko, P.P.2    Lysenko, Ju.V.3
  • 4
    • 0343250848 scopus 로고    scopus 로고
    • The convergence of the Newton-Kantorovich method under Vertgeim conditions: A new improvement
    • De Pascale, E., Zabreiko, P. P. (1998). The convergence of the Newton-Kantorovich method under Vertgeim conditions: a new improvement. Z. Anal. Anwend. 17(No. 2):271-280.
    • (1998) Z. Anal. Anwend. , vol.17 , Issue.2 , pp. 271-280
    • De Pascale, E.1    Zabreiko, P.P.2
  • 5
    • 0006835019 scopus 로고
    • Über die lösung der in Banachschen raume definierten nichtlinearen gleichungen
    • Fenyö, I. (1954). Über die lösung der in Banachschen raume definierten nichtlinearen gleichungen. Acta. Math. Acad. Sci. Hungar. 5:85-93.
    • (1954) Acta. Math. Acad. Sci. Hungar. , vol.5 , pp. 85-93
    • Fenyö, I.1
  • 6
    • 0004132033 scopus 로고
    • Functional analysis
    • (in Russian). Nauka, Moscow [(1982). Engl. Transl.: Pergamon Press, Oxford]
    • Kantorovich, L. V., Akilov, G. P. (1982). Functional analysis (in Russian). Nauka, Moscow [(1982). Engl. Transl.: Pergamon Press, Oxford].
    • (1982)
    • Kantorovich, L.V.1    Akilov, G.P.2
  • 7
    • 0003568896 scopus 로고
    • Approximate solutions of operator equations
    • (in Russian). Nauka, Moscow [(1972). Engl. Transl.: Noordhoff-Groningen]
    • Krasnosel'skij, M. A., Vajnikko, G. M., Zabreiko, P. P., Rutitskij, Ja. B., Stetsenko, V. Ja. (1966). Approximate solutions of operator equations (in Russian). Nauka, Moscow [(1972). Engl. Transl.: Noordhoff-Groningen].
    • (1966)
    • Krasnosel'skij, M.A.1    Vajnikko, G.M.2    Zabreiko, P.P.3    Rutitskij, Ja.B.4    Stetsenko, V.Ja.5
  • 8
    • 0006833092 scopus 로고
    • Conditions for the convergence of the Newton-Kantorovich method for nonlinear equations with Hölder linearizations
    • (in Russian)
    • Lysenko, J. V. (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).
    • (1994) Dokl. Akad. Nauk BSSR , vol.38 , pp. 20-24
    • Lysenko, J.V.1
  • 9
    • 0006838912 scopus 로고
    • On conditions for the applicability of Newton's method
    • (in Russian)
    • Vertgeim, B. A. (1956). On conditions for the applicability of Newton's method. Dokl. Akad. Nauk. SSSR 110:719-722 (in Russian).
    • (1956) Dokl. Akad. Nauk. SSSR , vol.110 , pp. 719-722
    • Vertgeim, B.A.1
  • 10
    • 0346751430 scopus 로고
    • On some methods of the approximate solution of nonlinear functional equations in Banach spaces
    • (in Russian) [(1960). Engl. Transl.: Amer. Math. Soc. Transl. 16(2):378-382]
    • Vertgeim, B. A. (1957). On some methods of the approximate solution of nonlinear functional equations in Banach spaces. Uspekhi Mat. Nauk. 12:166-169 (in Russian) [(1960). Engl. Transl.: Amer. Math. Soc. Transl. 16(2):378-382].
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    • Vertgeim, B.A.1
  • 11
    • 0034546528 scopus 로고    scopus 로고
    • Historical developments in convergence analysis for Newton's and Newton-like methods
    • Yamamoto, T. (2000). Historical developments in convergence analysis for Newton's and Newton-like methods. J. Comput. Appl. Math. 124:1-23.
    • (2000) J. Comput. Appl. Math. , vol.124 , pp. 1-23
    • Yamamoto, T.1
  • 12
    • 0023344904 scopus 로고
    • The majorant method in the theory of Newton-Kantorovich approximations and the Pták error estimates
    • Zabreiko, P. P., Nguen, D. F. (1987). The majorant method in the theory of Newton-Kantorovich approximations and the Pták error estimates. Numer. Funct. Anal. and Optimiz. 9(5&6):671-684.
    • (1987) Numer. Funct. Anal. and Optimiz. , vol.9 , Issue.5-6 , pp. 671-684
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* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.