# An algorithm in the solving of equations by interpolation

## 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
(Tiberiu Popoviciu Institute of Numerical Analysis)

## 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

## PDF

##### 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.

## References

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