Affordable Access

Publisher Website

The Bernstein Constant and Polynomial Interpolation at the Chebyshev Nodes

Authors
Journal
Journal of Approximation Theory
0021-9045
Publisher
Elsevier
Publication Date
Volume
119
Issue
2
Identifiers
DOI: 10.1006/jath.2002.3729
Keywords
  • Lagrange Interpolation
  • Chebyshev Nodes
  • Bernstein Constant.

Abstract

Abstract In this paper, we establish new asymptotic relations for the errors of approximation in L p [−1,1], 0< p⩽∞, of ∣ x∣ λ , λ>0, by the Lagrange interpolation polynomials at the Chebyshev nodes of the first and second kind. As a corollary, we show that the Bernstein constant B λ,p≔lim n→∞n λ+1/p inf c k ∥∣x∣ λ− ∑ k=0 nm c kx k∥ L p[−1,1] is finite for λ>0 and p∈ 1 3 ,∞) .

There are no comments yet on this publication. Be the first to share your thoughts.