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Volumn 79, Issue 1, 1997, Pages 131-145

A new semilocal convergence theorem for Newton's method

Author keywords

Convergence theorem; Error estimates; Majorizing sequences; Newton's method; Nonlinear equations in Banach spaces

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; DIFFERENTIAL EQUATIONS; ERROR ANALYSIS; MATHEMATICAL OPERATORS;

EID: 0031550718     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-0427(97)81611-1     Document Type: Article
Times cited : (100)

References (13)
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    • Argyros, I.K.1
  • 2
    • 0041600604 scopus 로고
    • A Newton-like method for solving nonlinear equations in Banach space
    • I.K. Argyros, A Newton-like method for solving nonlinear equations in Banach space, Acta Math. Hungh. 27 (1992) 368-378.
    • (1992) Acta Math. Hungh. , vol.27 , pp. 368-378
    • Argyros, I.K.1
  • 5
    • 38249006181 scopus 로고
    • A note on the Kantorovich theorem for Newton iteration
    • Z. Huang, A note on the Kantorovich theorem for Newton iteration, J. Comput. Appl. Math. 47 (1993) 211-217.
    • (1993) J. Comput. Appl. Math. , vol.47 , pp. 211-217
    • Huang, Z.1
  • 6
    • 0004972571 scopus 로고
    • On Newton's method for functional equations
    • L.V. Kantorovich, On Newton's method for functional equations, Dokl. Akad. Nauk SSRR 59 (1948) 1237-1240.
    • (1948) Dokl. Akad. Nauk SSRR , vol.59 , pp. 1237-1240
    • Kantorovich, L.V.1
  • 7
    • 0002865409 scopus 로고
    • The majorant principle and Newton's method
    • L.V. Kantorovich, The majorant principle and Newton's method, Dokl. Akad. Nauk SSRR 76 (1951) 17-20.
    • (1951) Dokl. Akad. Nauk SSRR , vol.76 , pp. 17-20
    • Kantorovich, L.V.1
  • 10
    • 51249194659 scopus 로고
    • Quadratic equations in Banach spaces
    • L.B. Rall, Quadratic equations in Banach spaces, Rend. Circ., Mat. Palermo (2) 10 (1961) 314-332.
    • (1961) Rend. Circ., Mat. Palermo , vol.10 , Issue.2 , pp. 314-332
    • Rall, L.B.1
  • 12
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    • A unified convergence theory for a class of iterative process
    • W.C. Rheinboldt, A unified convergence theory for a class of iterative process, SIAM J. Numer. Anal. 5 (1968) 42-63.
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    • Rheinboldt, W.C.1
  • 13
    • 0000205950 scopus 로고
    • A method for finding sharp error bounds for Newton's method under the Kantorovich assumptions
    • T. Yamamoto, A method for finding sharp error bounds for Newton's method under the Kantorovich assumptions, Numer. Math. 49 (1986) 203-220.
    • (1986) Numer. Math. , vol.49 , pp. 203-220
    • Yamamoto, T.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.