Access the full text.
Sign up today, get DeepDyve free for 14 days.
Loading next page...
/lp/springer-journals/recurrence-relations-for-chebyshev-type-methods-t2TV8v4d9y
References (7)
-
(1988)
Estimadores a priori del error para los m ́ etodos iterativos de Halley y de Chebyshev -
Tetsuro Yamamoto (1986)
A method for finding sharp error bounds for Newton's method under the Kantorovich assumptionsNumerische Mathematik, 49
-
I. Argyros, Dong Chen (1993)
Results on the Chebyshev method in banach spacesProyecciones (antofagasta), 12
-
(1988)
Estimadores a priori del error para los métodos iterativos de Halley y de Chebyshev -
J. Ortega, W. Rheinboldt (2014)
Iterative solution of nonlinear equations in several variables -
L. Rall (1961)
Quadratic equations in Banach spacesRendiconti del Circolo Matematico di Palermo, 10
-
J. Ó, L. Rall (1969)
Computational Solution of Nonlinear Operator Equations
- Publisher
- Springer Journals
- Copyright
- 2000 Springer-Verlag New York Inc.
- Subject
- Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics, Simulation
- ISSN
- 0095-4616
- eISSN
- 1432-0606
- DOI
- 10.1007/s002459911012
- Publisher site
- See Article on Publisher Site
Abstract
Abstract. The convergence of new second-order iterative methods are analyzed in Banach spaces by introducing a system of recurrence relations. A system of a priori error bounds for that method is also provided. The methods are defined by using a constant bilinear operator A , instead of the second Fréchet derivative appearing in the defining formula of the Chebyshev method. Numerical evidence that the methods introduced here accelerate the classical Newton iteration for a suitable A is provided.
Journal
Applied Mathematics and Optimization – Springer Journals
Published: Apr 1, 2000