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
(Tiberiu Popoviciu Institute of Numerical Analysis)
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.
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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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References
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[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.