Numerische Mathematik

, Volume 78, Issue 1, pp 59–85

Polynomial interpolation of minimal degree

  • Thomas Sauer

DOI: 10.1007/s002110050304

Cite this article as:
Sauer, T. Numer. Math. (1997) 78: 59. doi:10.1007/s002110050304

Summary.

Minimal degree interpolation spaces with respect to a finite set of points are subspaces of multivariate polynomials of least possible degree for which Lagrange interpolation with respect to the given points is uniquely solvable and degree reducing. This is a generalization of the concept of least interpolation introduced by de Boor and Ron. This paper investigates the behavior of Lagrange interpolation with respect to these spaces, giving a Newton interpolation method and a remainder formula for the error of interpolation. Moreover, a special minimal degree interpolation space will be introduced which is particularly beneficial from the numerical point of view.

Mathematics Subject Classification (1991): 65D10, 41A05, 41A10

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Thomas Sauer
    • 1
  1. 1. Mathematical Institute, University Erlangen–Nuremberg, Bismarckstr. 1 1/2, D-90537 Erlangen, Germany; e-mail: sauer@mi.uni-erlangen.de DE