On multivariate Lagrange interpolation
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- by Thomas Sauer and Yuan Xu PDF
- Math. Comp. 64 (1995), 1147-1170 Request permission
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 $(n + 1)$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.References
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Additional Information
- © Copyright 1995 American Mathematical Society
- 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