Interpolation de Lagrange

To our knowledge Lagrange interpolation was first used for fractional delay approx- imation by Strube (1975) who derived it using the Taylor series approach.

Barycentric interpolation is a variant of Lagrange polynomial interpolation that is fast and †Département de Mathématiques Université de Fribourg

mine the structure of the interpolating polynomial. [4] C. HERMITE Sur la formule d'interpolation de Lagrange

Définition 5 – Ce polynôme s'appelle l'interpolant de la fonction f de degré n aux points x0 x1

Lagrange Interpolation: Introduction I. Consider the example we were considering in the previous lecture. The secret was s = 3. Secret shares of party 1 2

1.polynôme de Lagrange. 2.calcul de dérivées : différences finies. 3.calcul d'intégrales : quadrature d'interpolation. 4.intégration temporelle d'EDO's 

Lagrange interpolation by polynomials in several variables is stud- approach has been given by de Boor and Ron (see [1] and the references therein).

+ 1 distinct numbers and let () be a function de ned on a Example We will use Lagrange interpolation to find the unique polynomial 3()

The purpose of this paper is to give an explicit multivariate analogue of Lagrange's formula under conditions which we will specify. 2 Polynomial Interpolation.

convergence of Lagrange interpolation based at the zeros of slightly Sur le mode de convergence pour l'interpolation de Lagrange C. R. Acad.

Lagrange Interpolation Calculus provides many tools that can be used to understand the behavior of functions but in most cases it is necessary for these functions to be continuous or di erentiable This presents a problem in most real" applications in which functions are used to model relationships between quantities

Lagrange Interpolation The basic principle of polynomial interpolation is that we “take measurements” offby looking at the values of the function (and its derivatives) at certain points We then construct a polynomial that satis˜es the same measurements

This is theLagrange formof the interpolating polynomial To construct it observe that it su ces to nd polynomialsLi such that Li has degreen Li(xi) = 1 Li(xj) = 0 forj6=i Property (iii) can be satis ed by constructing a polynomial with roots atxj forj6=i(therearenof them so (i) is not a concern): Li(x) =c(x j6=i xj):

LAGRANGE INTERPOLATION • Fit points with an degree polynomial • = exact function of which only discrete values are known and used to estab-lish an interpolating or approximating function • = approximating or interpolating function This function will pass through all specified interpolation points (also referred to as data points or nodes)

LAGRANGE INTERPOLATION AND FINITE ELEMENT SUPERCONVERGENCE BO LI Abstract Weconsiderthe niteelementapproximationoftheLaplacianoperator with the homogeneous Dirichlet boundary condition and study the corresponding Lagrange interpolation in the context of nite element superconvergence For d-

One of the methods used to find this polynomial is called the Lagrangian method of interpolation Other methods include Newton’s divided difference polynomial method and the direct method We discuss the Lagrangian method in this chapter 05 05 1 The Lagrangian interpolating polynomial is given by n f(x) L i(x)f(x) 0