On an application of Newton's method to nonlinear operators with w-conditioned second derivative

BIT Numerical Mathematics

Volumn 42, Issue 3, 2002, Pages 519-530

  Ezquerro, J A ^a   Hernandez M A ^a  

^a UNIVERSITY OF LA RIOJA   (Spain)

Author keywords

Convergence theorem; Integral equation; Newton's method; Nonlinear equations in Banach spaces; Recurrence relations

Indexed keywords

EID: 0042735343     PISSN: 00063835     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1021977126075     Document Type: Article

References (6)

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2. M. A. Hernández, The Newton method for operators with Hölder continuous first derivative, J. Optim. Theory Appl., 109 (2001), pp. 631-648.
3. L. V. Kantorovich, Functional Analysis and Applied Mathematics, Report 1509, National Bureau of Standards, 1952.
4. H. Keller, Numerical Methods for Two-Point Boundary Value Problems, Dover, New York, 1992.
5. J. M. Ortega, The Newton-Kantorovich theorem, Amer. Math. Monthly, 75 (1968), pp. 658-660.
6. J. Rokne, Newton's method under mild differentiability conditions with error analysis, Numer. Math., 18 (1972), pp. 401-412.