## 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

[1] I.G. Berezin, P.N. Zidkov, *Metody vycislenii*, I. Moskow, 1962.

[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.

Scanned paper.

## About this paper

##### 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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