On multivariate Lagrange interpolation

Authors:
Thomas Sauer and Yuan Xu

Journal:
Math. Comp. **64** (1995), 1147-1170

MSC:
Primary 41A63; Secondary 41A05, 65D05

DOI:
https://doi.org/10.1090/S0025-5718-1995-1297477-5

MathSciNet review:
1297477

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Abstract | References | Similar Articles | Additional Information

Abstract: 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 *n* of a function *f*, which is a sum of integrals of certain st directional derivatives of *f* 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.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1995-1297477-5

Keywords:
Lagrange interpolation,
finite difference,
simplex spline,
remainder formula,
algorithm

Article copyright:
© Copyright 1995
American Mathematical Society