Solving equations by Hermite type inverse interpolation

Abstract

We study the convergence of an iterative method for solving the equation (fleft( xright) =0, f:Isubseteq mathbb{Rrightarrow R}). The iterative method is obtained by the Hermite inverse interpolation polynomial. We show that the convergence order of this method is given by the unique positive solution of a polynomial equation with coefficients given by the multiplicity orders. We consider the particular instance of two interpolation nodes and we determine the resulted methods.

Authors

Crăciun Iancu, Ion Păvăloiu

Title

Original title (in French)

La resolution des équations par interpolation inverse de type Hermite

English translation of the title

Solving equations by Hermite inverse interpolation

Keywords

Hermite interpolation; inverse interpolation; nonlinear equations in R; iterative methods; multistep method; convergence order

References

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[2] Gh. Coman, Some practical approximation methods for nonlinear equations, Anal. Numer. Theor. Approx., 11, 1-2, (1982), 41–48.

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

[4] I. Pavaloiu, Rezolvarea ecua¸iilor prin interpolare, Ed. Dacia, 1981.

[5] I. Pavaloiu, Introducere in aproximarea solutiilor ecuatiilor, Ed. Dacia, 1976.

[6] D.D. Stancu, Asupra formulei de interpolare a lui Hermite si a unor aplicatii ale acesteia, Studii ¸si Cercet. Mat. (Cluj), 3-4 VIII, (1957), 339-355.

[7] J.F. Traub, Iterative Methods for the Solution of Equations, Prentice Hall Series in Automatic Computation 1964.

[8] B.A. Turowicz, Sur les derivees d’ordre superiour d’une fonction inverse, Colloq. Math., (1959), 83–87.

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Cite this paper as:

C. Iancu, I. Păvăloiu, La resolution des équations par interpolation inverse de type Hermite, Mathematica (Cluj), 26(49) (1984) no. 2, pp. 115-123 (in French).

Journal

Mathematica

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