## Abstract

Consider the nonlinear equation in \(R\), \(f\left( x\right) =0\), where \(f:A\rightarrow B \), \((A,B\subseteq \mathbb{R})\) which is assumed bijective. The Lagrange inverse interpolation polynomial leads to an iterative method of the form \[x_{i+n+2}=L_{n}[ y_{i+1},y_{i+2},…,y_{i+n+1}:f_{|0}^{-1}],\ \quad x_{1},x_{2},…,x_{n+1}\in I.\] At each iterative step we need to compute the values \(\omega_{k}\left( x\right) \) and \(\omega_{k}^{\prime}\left( y_{i}\right) ,\ i=k,\ldots,k+n\), where \(\omega_{k}\left( y\right) =\Pi_{i=k}^{k_{n}}\left( y-y_{k}\right) \). We give an algorithm for computing \(\omega_{k+1}\left( 0\right) \) and \(\omega_{k+1}^{\prime}\left( y_{i}\right) \) using \(\omega_{k}\left(0\right) \) and \(\omega_{k}^{\prime}\left( y\right) \).

## Authors

Ion Păvăloiu

## Title

### Original title (in French)

*Un algorythme de calcul dans la résolution des equations par interpolation*

### English translation of the title

*An algorithm in the solving of equations by interpolation*

## Keywords

nonlinear equation in \(\mathbb{R}\); inverse interpolation; iterative method; Lagrange polynomial; inverse Lagrange interpolation polynomial

## References

[1] I. Pavaloiu, *Rezolvarea ecuatiilor prin interpolare*, Editura Dacia, Cluj-Napoca, 1981.

Scanned paper.

## About this paper

##### Cite this paper as:

I. Păvăloiu, *Un algorythme de calcul dans la résolution des equations par interpolation*, Seminar on functional analysis and numerical methods. Preprint no. 1 (1987), pp. 130-134 (in French).

##### Journal

Seminar on functional analysis and numerical methods,

Preprint

##### Publisher Name

“Babes-Bolyai” University,

Faculty of Mathematics,

Research Seminars

##### DOI

Not available yet.