On multivariate Hermite interpolation

Abstract  We study the problem of Hermite interpolation by polynomials in several variables. A very general definition of Hermite interpolation
is adopted which consists of interpolation of consecutive chains of directional derivatives. We discuss the structure and
some aspects of poisedness of the Hermite interpolation problem; using the notion of blockwise structure which we introduced
in [10], we establish an interpolation formula analogous to that of Newton in one variable and use it to derive an integral
remainder formula for a regular Hermite interpolation problem. For Hermite interpolation of degreen of a functionf, the remainder formula is a sum of integrals of certain (n + 1)st directional derivatives off multiplied by simplex spline functions.

• Content Type Journal Article
• DOI 10.1007/BF03177515
• Authors
  
  
  • Thomas Sauer, University Erlangen-Nuremberg Mathematical Institute D-91054 Erlangen Germany
  • Yuan Xu, University of Oregon Department of Mathematics 97403 Eugene OR USA
  
  

• Journal Advances in Computational Mathematics
• Online ISSN 1572-9044
• Print ISSN 1019-7168




• Journal Volume Volume 4




• Journal Issue Volume 4, Number 1 / December, 1995

Published by

Original source : http://www.springerlink.com/content/u76137675655r5...