Reduced recurrence relations for the Chebyshev method

Journal of Optimization Theory and Applications

Volumn 98, Issue 2, 1998, Pages 385-397

  Hernandez M A ^a  

^a UNIVERSITY OF LA RIOJA   (Spain)

Author keywords

Chebyshev method; Nonlinear equations in Banach spaces; Recurrence relations; Third order methods

Indexed keywords

BANACH SPACES; NONLINEAR EQUATIONS;

CHEBYSHEV'S METHODS; CONDITION; HALLEY'S METHOD; NEWTON'S METHODS; NONLINEAR EQUATIONS IN BANACH SPACES; RECURRENCE RELATIONS; THIRD ORDER METHODS;

NEWTON-RAPHSON METHOD;

EID: 0039401851     PISSN: 00223239     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1022641601991     Document Type: Article

References (18)

1. ARGYROS, I. K., and CHEN, D., Results on the Chebyshev Method in Banach Spaces, Proyecciones, Vol. 12, pp. 119-128, 1993.
2. CANDELA, V., and MARQUINA, A., Recurrence Relations for Rational Cubic Methods, II: The Chebyshev Method, Computing, Vol. 45, pp. 355-367, 1990.
3. ALTMAN, M., Concerning the Method of Tangent Hyperbolas for Operator Equations, Bulletin de L'Academie Polonaise des Sciences, Série des Sciences Mathématiques, Astronomie, et Physique, Vol. 9, pp. 633-637, 1961.
4. CANDELA, V., and MARQUINA, A., Recurrence Relations for Rational Cubic Methods, I: The Halley Method, Computing, Vol. 44, pp. 169-184, 1990.
5. HERNANDEZ, M. A., A Note on Halley's Method, Numerische Mathematik, Vol. 59, pp. 273-276, 1991.
6. CHEN, D., ARGYROS, I. K., and QIAN, Q. S., A Local Convergence Theorem for the Super-Halley Method in Banach Spaces, Applied Mathematics Letters, Vol. 7, pp. 49-52, 1994.
7. HERNANDEZ, M. A., Newton-Raphson Method and Convexity, Zbornik Radova Prirodno-Matematičkog Fakulteta Univerziteta u Novom Sadu, Serija Za Matematiku, Vol. 22, pp. 159-166, 1993.
8. KANTOROVICH, L. V., and AKILOV, G. P., Functional Analysis, Pergamon Press, Oxford, England, 1982.
9. TAPIA, R. A., The Kantorovich Theorem for the Newton Method, American Mathematical Monthly, Vol. 78, pp. 389-392, 1971.
10. GUTIERREZ, J. M., and HERNANDEZ, M. A., A Family of Chebyshev-Halley Type Methods in Banach Spaces, Bulletin of the Australian Mathematical Society, Vol. 55, pp. 113-130, 1997.
11. KANTOROVICH, L. V., On the Newton Method for Functional Equations, Doklady Akademii Nauk SSSR, Vol. 59, pp. 1237-1240, 1948.
12. KANTOROVICH, L. V., The Majorant Principle for the Newton Method, Doklady Akademii Nauk SSSR, Vol. 76, pp. 17-20, 1951.
13. YAMAMOTO, T., A Method for Finding Sharp Error Bounds for the Newton Method under the Kantorovich Assumptions, Numerische Mathematik, Vol. 49, pp. 203-220, 1986.
14. DÖRING, B., Einige Sätze über das Verfahren der Tangierenden Hyperbeln in Banach-Räumen, Aplikace Mathematiky, Vol. 15, pp. 418-464, 1970.
15. RALL, L. B., Computational Solution of Nonlinear Operator Equations, Robert E. Krieger Publishing Company, New York, New York, 1979.
16. SMALE, S., Newton Method Estimates from Data at One Point, Proceedings of a Conference in Honor of Gail Young, Laramie, New York, Vol. 2, pp. 1-16, 1986.
17. YAKOUBSOHN, J. C., Une Constante Universelle pour la Convergence de la Méthode de Newton, Comptes Rendus de l'Academie des Sciences de Paris, Série I, Vol. 320, pp. 385-390, 1995.
18. ZHENG, S., Point Estimates for Halley's Iteration, Acta Mathematica Applicatae Sinica, Vol. 14, pp. 376-383, 1991.