On Newton's method under mild differentiability conditions and applications

Applied Mathematics and Computation

Volumn 102, Issue 2-3, 1999, Pages 177-183

  Argyros, Ioannis K ^a  

^a CAMERON UNIVERSITY   (United States)

Author keywords

47H17; 49D15; 65J15; Banach space; Fr chet derivative; H lder continuity; Lipschitz conditions; Majorant theory; Newton method

Indexed keywords

EID: 0001298745     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0096-3003(98)10014-0     Document Type: Article

References (8)

1. I.K. Argyros, F. Szidarovszky, The Theory and Applications of Iteration Methods, CRC Press, Boca Raton, Florida, 1993.
2. J.M. Ortega, W.C. Rheinboldt, Iterative Solution of Nonlinear Equations in Several Variables, Academic Press, New York, 1970.
3. Argyros I.K. On Newton's method and nondiscrete mathematical induction. Bull. Austral. Math. Soc. 38:1988;131-140.
4. Galperin A., Waksman Z. Newton's method under weak smoothness assumptions. J. Comput. Appl. Math. 35:1991;207-215.
5. Galperin A., Waksman Z. Regular smoothness and Newton's method. Numer. Funct. Anal. Optim. 15(7/8):1994;813-858.
6. S. Chandrasekhar, Radiative Transfer, Dover, New York, 1960.
7. Rheinboldt W.C. A unified convergence theory for a class of iterative processes. SIAM J. Numer. Anal. 5(1):1968;42-63.
8. Argyros I.K. A convergence theorem for Newton-like methods under generalized Chen-Yamamoto-type assumptions. Appl. Math. Comput. 61(1):1994;121-137.