Sur quelques méthodes itératives de type interpolatoire à vitesse de convergence optimale
On some iterative methods of interpolatory type with optimal convergence rate
Abstract
We consider nonlinear equations in \(\mathbb{R}\), and a class of iterative methods obtained by inverse interpolation of Hermite type. We determine the methods with the highest convergence order among the methods in the considered class.
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References
Ostrowski, A. M., Solution of equations and systems of equations. Pure and Applied Mathematics, Vol. IX. Academic Press, New York-London 1960 ix+202 pp., MR0127525.
Păvăloiu, I., Rezolvarea ecuaţiilor prin interpolare, Ed. DACIA, 1981.
Iancu, C.; Păvăloiu, I., La résolution des équations par interpolation inverse de type Hermite. (French) [Solution of equations by inverse interpolation of Hermite type] Seminar of Functional Analysis and Numerical Analysis, pp. 72-84, Preprint 1981, 4, Univ. "Babeş-Bolyai", Cluj-Napoca, 1981, MR0671746.
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