A Constructive Approach to Kergin Interpolation in R(k).

Abstract

Very little seems to be known about polynomial interpolation of multivariate functions. However, Kergin recently established the existence and uniqueness of a natural extension of univariate interpolation to a multivariate setting. In this paper we provide a formula for Kergin interpolation. This formula is based on the Newton form for univariate polynomial interpolation. The error in approximating by Kergin interpolation is also obtained in a convenient form which allows us to assess the quality of this scheme. In particular, we establish that Kergin interpolation converges for analytic functions of several variables.

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Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1978
Accession Number
ADA063996

Entities

People

  • Charles A. Micchelli

Organizations

  • University of Wisconsin–Madison

Tags

DTIC Thesaurus Topics

  • Algebra
  • Analytic Functions
  • Continents
  • Convex Sets
  • Equations
  • Identities
  • Integrals
  • Interpolation
  • Mathematical Analysis
  • Mathematics
  • Military Research
  • North Carolina
  • Polynomials
  • Sequences
  • Theorems
  • United States
  • Wisconsin

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Statistical inference.