## Abstract

We consider optimality problems regarding the order of convergence of the iterative methods which are obtained by inverse interpolation of Lagrange-Hermite type. A similar problem for a class of Steffensen-type methods is solved.

## Authors

Ion Păvăloiu

## Title

*Optimal problems concerning interpolation methods of solution of equations*

## Keywords

nonlinear equations in R; order of convergence; iterative methods; inverse interpolation; Lagrange-Hermite; Steffensen-type methods.

## References

[1] C. Iancu, I. Pavaloiu, *La resolution des equations par interpolation inverse de type Hermite*, Mathematica 26(49) (1984) no. 2, 115–123.

[2] C. Iancu, I. Pavaloiu, I. Serb. *Methodes iteratives optimales de type Steffensen obtenues par interpolation inverse*, Research Seminar on Functional analysis and Numerical Methods, Preprint 1 (1983), 81–88.

[3] M. A. Ostrowski, *Solution of Equations and Systems of Equations*, Academic Press, New York and London, 1980.

[4] I. Pavaloiu, *Solving the Equations by Interpolation*, Dacia, Cluj-Napoca, 1981, (in Romanian).

[5] J.F. Steffensen, *Interpolation*, Chelsea Publ., New York, 1950.

[6] J.F. Traub, *Iterative Methods for the Solution of Equation*, Prentice-Hall, Englewood Cliffs, N.J., 1964.

[7] B.A. Turowicz, *Sur les deriv´ees d’ordre superiour d’une fonction inverse*, Ann. Polon. Math. 8 (1960), 265–269.

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## About this paper

##### Cite this paper as:

I. Păvăloiu, *Optimal problems concerning interpolation methods of solution of equations*, Publications de L’Institut Mathématique (Nouvelle série) Beograd, **52(66)** (1992), pp. 113-126

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Publications de L’Institut Mathématique (Nouvelle série) Beograd

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