On some interpolation iterative methods with optimal convergence speed

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.

Ion Păvăloiu

I. Şerb

Original title (in French)

Sur quelques méthodes itératives de type intérpolatoire à vitèsse de convergence optimale

English translation of the title

On some inverse interpolation iterative methods with optimal convergence speed

Keywords: inverse interpolation; Hermite polynomial; inverse Hermite interpolation; iterative method; convergence order

[1] Ostrowski, M. A., Solution of Equations and Systems of Equations, Academic Press, New-York and London, 1960.

[2] Pavaloiu, I., Rezolvarea ecuatiilor prin interpolare, Ed. Dacia, 1981.

[3] Pavaloiu, I., Iancu, C., La resolution des equations par interpolation inverse de type Hermite, Seminar of functional analysis and Numerical methods, ”Babes-Bolyai” University, Research Seminaries, Preprint Nr. 4, (1981), 72–84. republished in: Mathematica (Cluj), 26(49) (1984), no. 2, pp. 115–123.

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I. Păvăloiu, I. Şerb, Sur quelques méthodes itératives de type intérpolatoire à vitèsse de convergence optimale, Anal. Numér. Théor. Approx., 12 (1983) no. 1, pp. 83-88 (in French).

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