On Multivariate Lagrange Interpolation
نویسنده
چکیده
Lagrange interpolation by polynomials in several variables is studied through a finite difference approach. We establish an interpolation formula analogous to that of Newton and a remainder formula, both of them in terms of finite differences. We prove that the finite difference admits an integral representation involving simplex spline functions. In particular, this provides a remainder formula for Lagrange interpolation of degree « of a function /, which is a sum of integrals of certain (n + l)st directional derivatives of / multiplied by simplex spline functions. We also provide two algorithms for the computation of Lagrange interpolants which use only addition, scalar multiplication, and point evaluation of polynomials.
منابع مشابه
MEAN VALUE INTERPOLATION ON SPHERES
In this paper we consider multivariate Lagrange mean-value interpolation problem, where interpolation parameters are integrals over spheres. We have concentric spheres. Indeed, we consider the problem in three variables when it is not correct.
متن کاملOn Lagrange multivariate interpolation problem in generalized degree polynomial spaces
The aim of this paper is to study the Lagrange multivariate interpolation problems in the space of polynomials of w-degree n. Some new results concerning the polynomial spaces of w-degree n are given. An algorithm for obtaining the w-minimal interpolation space is presented. Key–Words: Lagrange multivariate polynomial interpolation, whomogeneous polynomial spaces, Generalize degree.
متن کاملUNIVERSITY OF WISCONSIN-MADISON CENTER FOR THE MATHEMATICAL SCIENCES A multivariate form of Hardy's inequality and Lp-error bounds for multivariate Lagrange interpolation schemes
valid for f 2 Lp(IR ) and an arbitrary nite sequence of points in IR, is discussed. The linear functional f 7! R f was introduced by Micchelli [M80] in connection with Kergin interpolation. This functional also naturally occurs in other multivariate generalisations of Lagrange interpolation, including Hakopian interpolation, and the Lagrange maps of Section 5. For each of these schemes, (1) imp...
متن کاملOn the approximation of multivariate entire functions by Lagrange interpolation polynomials
We show that the intertwining of sequences of good Lagrange interpolation points for approximating entire functions is still a good sequence of interpolation points. We give examples of such sequences.
متن کاملA Multivariate Form of Hardy's Inequality and L P -error Bounds for Multivariate Lagrange Interpolation Schemes
The following multivariate generalisation of Hardy's inequality, that for m ? n=p > 0
متن کامل