On the radius of convergence of Newton's method

International Journal of Computer Mathematics

Volumn 77, Issue 3, 2001, Pages 389-400

  Argyros, Ioannis K ^a  

^a CAMERON UNIVERSITY   (United States)

Author keywords

Affine invariant operator; Banach space; Newton's method; Predictor corrector procedure; Radius of convergence

Indexed keywords

AFFINE INVARIANT; LIPSCHITZ; NEWTON'S METHODS; PREDICTOR CORRECTOR; PREDICTOR CORRECTOR PROCEDURE; RADIUS OF CONVERGENCE; SEMI-LOCAL CONVERGENCES;

BANACH SPACES;

NEWTON-RAPHSON METHOD;

EID: 10144231902     PISSN: 00207160     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (8)

1. Argyros, I. K. (1990). Error bounds for the modified Secant method, BIT, 30, 92-100.
2. Argyros, I. K. (1990). On the solution of equations with nondifferentiable operators and Ptak error estimates, BIT, 30, 752-754.
3. Argyros, I. K. and Szidarovszky, F., The Theory and Application of Iteration Methods, CRC Press, Inc., Boca Raton, Florida, 1993.
4. Deuflhard, P. (1979). A stepsize control for continuation methods and its special applications to multiple shooting techniques, Numer. Math., 33, 115-146.
5. Gutierez, J. (1997). A new semilocal convergence theorem for Newton's method, J. Comp. Appl. Math., 79, 131-145.
6. Hackl, J., Wacker, H. and Zulehner, W. (1980). An efficient stepsize control for continuation methods, BIT, 20, 475-485.
7. Kantorovich, L. V. and Akilov, G. P., Functional Analysis, Pergamon Press, Oxford, 1982.
8. Ypma, T. J. (1982). Affine invariant convergence results for Newton's method, BIT, 22, 108-118.