The Divergence of Lagrange Interpolation for |x|α at Equidistant Nodes
✍ Scribed by Michael Revers
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 136 KB
- Volume
- 103
- Category
- Article
- ISSN
- 0021-9045
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📜 SIMILAR VOLUMES
It is a classical result of Bernstein that the sequence of Lagrange interpolation polynomials to \(|x|\) at equally spaced nodes in \([-1,1]\) diverges everywhere, except at zero and the end-points. In the present paper we show that the case of equally spaced nodes is not an exceptional one in this
We establish pointwise as well as uniform estimates for Lebesgue functions associated with a large class of Erdo s weights on the real line. An Erdo s weight is of the form W :=exp(&Q), where Q : R Ä R is even and is of faster than polynomial growth at infinity. The archetypal examples are where Q