Concerning the radius of convergence of Newton's method and applications

Journal of Applied Mathematics and Computing

Volumn 6, Issue 3, 1999, Pages 451-462

  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

BANACH SPACES;

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

NEWTON-RAPHSON METHOD;

EID: 0006518075     PISSN: 15985865     EISSN: None     Source Type: Journal    
DOI: 10.1007/bf03009941     Document Type: Article

References (8)

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