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Volumn 17, Issue 2, 1998, Pages 271-280

Convergence of the Newton-Kantorovich method under vertgeim conditions: A new improvement

Author keywords

H lder type conditions; Newton Kantorovich approximations

Indexed keywords


EID: 0343250848     PISSN: 02322064     EISSN: None     Source Type: Journal    
DOI: 10.4171/ZAA/821     Document Type: Article
Times cited : (24)

References (14)
  • 1
    • 0030622898 scopus 로고    scopus 로고
    • New results on Newton - Kantorovich approximations with applications to nonlinear integral equations
    • Appell, J., De Pascale, E., Lysenko, Ju. V. and P. P. Zabreiko: New results on Newton - Kantorovich approximations with applications to nonlinear integral equations. Numer. Funct. Anal. Optim. 18 (1997), 1 - 18.
    • (1997) Numer. Funct. Anal. Optim. , vol.18 , pp. 1-18
    • Appell, J.1    De Pascale, E.2    Lysenko, Ju.V.3    Zabreiko, P.P.4
  • 2
    • 84948517016 scopus 로고
    • On the application of the Newton - Kantorovich method to nonlinear integral equations of Uryson type
    • Appell, J., De Pascale, E. and P. P. Zabreiko: On the application of the Newton - Kantorovich method to nonlinear integral equations of Uryson type. Numer. Funct. Anal. Optim. 12 (1991), 271 - 283.
    • (1991) Numer. Funct. Anal. Optim. , vol.12 , pp. 271-283
    • Appell, J.1    De Pascale, E.2    Zabreiko, P.P.3
  • 3
    • 0346751436 scopus 로고
    • Some remarks on the Newton - Kantorovich method for nonlinear equations with Hölder continuous linearizations
    • Demidovich, N. T., Zabreiko, P. P. and Ju. V. Lysenko: Some remarks on the Newton - Kantorovich method for nonlinear equations with Hölder continuous linearizations (in Russian). Izv. Akad. Nauk Beloruss. 3 (1993), 22 - 26.
    • (1993) Izv. Akad. Nauk Beloruss. , vol.3 , pp. 22-26
    • Demidovich, N.T.1    Zabreiko, P.P.2    Lysenko, Ju.V.3
  • 4
    • 54649083302 scopus 로고    scopus 로고
    • New convergence criteria for the Newton - Kantorovich method and some applications to nonlinear integral equations
    • to appear
    • De Pascale, E. and P. P. Zabreiko: New convergence criteria for the Newton - Kantorovich method and some applications to nonlinear integral equations. Rend. Semin. Mat. Univ. Padova 100 (1998) (to appear).
    • (1998) Rend. Semin. Mat. Univ. Padova , vol.100
    • De Pascale, E.1    Zabreiko, P.P.2
  • 7
    • 0006833092 scopus 로고
    • Conditions for the convergence of the Newton - Kantorovich method for nonlinear equations with Holder linearizations
    • Lysenko, Ju. V.: Conditions for the convergence of the Newton - Kantorovich method for nonlinear equations with Holder linearizations (in Russian). Dokl. Akad. Nauk BSSR 38 (1994), 20 - 24.
    • (1994) Dokl. Akad. Nauk BSSR , vol.38 , pp. 20-24
    • Lysenko, Ju.V.1
  • 8
    • 4243155484 scopus 로고
    • Concerning the rate of convergence of Newton's process
    • Ptak, V.: Concerning the rate of convergence of Newton's process. Comm. Math. Univ. Carolinae 16 (1975), 699 - 705.
    • (1975) Comm. Math. Univ. Carolinae , vol.16 , pp. 699-705
    • Ptak, V.1
  • 10
    • 0002214493 scopus 로고
    • A unified convergence theory for a class of iterative processes
    • Rheinboldt, W. C.: A unified convergence theory for a class of iterative processes. SIAM J. Numer. Anal. 5 (1968), 42 - 63.
    • (1968) SIAM J. Numer. Anal. , vol.5 , pp. 42-63
    • Rheinboldt, W.C.1
  • 12
    • 0006838912 scopus 로고
    • On conditions for the applicability of Newton's method
    • Vertgeim, B. A.: On conditions for the applicability of Newton's method (in Russian). Dokl. Akad. Nauk SSSR 110 (1956), 719 - 722.
    • (1956) Dokl. Akad. Nauk SSSR , vol.110 , pp. 719-722
    • Vertgeim, B.A.1
  • 13
    • 0346751430 scopus 로고
    • On some methods of solution of nonlinear operator equations in Banach spaces
    • Vertgeim, B. A.: On some methods of solution of nonlinear operator equations in Banach spaces (in Russian). Uspekhi Mat. Nauk 12 (1957), 166 - 169.
    • (1957) Uspekhi Mat. Nauk , vol.12 , pp. 166-169
    • Vertgeim, B.A.1
  • 14
    • 4243153215 scopus 로고
    • Estimating the rate of convergence of the Newton - Kantorovich method for equations with Hölder linearizations
    • Zabrejko, P. P. and D. F. Nguyen: Estimating the rate of convergence of the Newton - Kantorovich method for equations with Hölder linearizations (in Russian). Izv. Akad. Nauk BSSR 2 (1991), 8 - 14.
    • (1991) Izv. Akad. Nauk BSSR , vol.2 , pp. 8-14
    • Zabrejko, P.P.1    Nguyen, D.F.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.