Posts by Ion Păvăloiu


The inverse interpolatory polynomials of Hermite type with 2 nodes, allhaving the same order of multiplicity \(q\in N\), provide a class of iterative methods for solvingscala-r’ equations. In this note we determine the iterative method with the highest efficiencyindex: the optimal method is obtained for \(q=2\).



Ion Păvăloiu
(Tiberiu Popoviciu Institute of Numerical Analysis)




Scanned paper: on the journal website.

PDF-LaTeX version of the paper (soon).

Cite this paper as:

I. Păvăloiu, Optimal efficiency index of a class of Hermite iterative methods with two steps, Rev. Anal. Numér. Théor. Approx., 29 (2000) no. 1, pp. 83-89.

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[1] BRENT, R., WINOGRAD, S., WOLFE, F., Optimal Iterative Processes for Root-Finding, Numer. Math., 20, pp.327-341, 1973.

[2] COMAN, GH., Some Practical Approximation Methods for nonlinear Equations, Matematica-Revue d’Analyse Numerique et de Theorie de l’Approximation, 11, no.1-2, pp.11-48, 1982.

[3] KUNG, H.T., TRAUB, J.F., Optimal Order and Efficiency for Iterations with Two Evaluations, SIAM J. Numer. Anal., 13, no.1, pp. 84-99, 1976.

[4] OSTROWSKI, A.M., Solution of Equation and Systems of Equations, Academic Press, New York and London, 1966.

[5] Păvăloiu, I., Bilateral Approximation for the Soltuions of Scalar Equations, Revue D’Analyse Numerique et de Theorie del’Approximation, 23, 1, pp.95-100, 1994.

[6] Păvăloiu,  I., Optimal Problems Concerning Interpolation Methods of Solutions of Equations, Publ. Inst. Math. 52 (66), pp.113-126, 1992.

[7] Păvăloiu,I., Optimal Efficiency Index for Iterative Methods of Interpolatory Type, Computer Science Journal of Moldova, 5, nr.1 (13), pp.20-43, 1997.

[8] TRAUB, J.F., Iterative methods for slution of equations, Prentice-Hall Inc., Englewood Cliffs, New Jersey, 1964.

[9] TUROWICZ, B.A., Sur les derivees d’ordre superieur d’une fonction inverse, Ann.Polon. Math., 8, pp.265-269, 1960.

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