Optimal problems concerning interpolation methods of solution of equations

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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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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