On the Divergence Phenomenon in Hermite–Fejér Interpolation
✍ Scribed by H.-P. Blatt; M. Götz
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 142 KB
- Volume
- 106
- Category
- Article
- ISSN
- 0021-9045
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📜 SIMILAR VOLUMES
Necessary conditions of normal pointsystems for Hermite-Fejér interpolation of arbitrary (even) order are given. In particular, one of the main results in this paper is: If a pointsystem consists of the zeros of orthogonal polynomials with respect to a weight w on [-1, 1] and is always normal for He
For f # C [&1, 1], let H m, n ( f, x) denote the (0, 1, ..., m) Hermite Feje r (HF) interpolation polynomial of f based on the Chebyshev nodes. That is, H m, n ( f, x) is the polynomial of least degree which interpolates f (x) and has its first m derivatives vanish at each of the zeros of the nth Ch
It is shown that the fundamental polynomials for (0, 1, ..., 2m+1) Hermite Feje r interpolation on the zeros of the Chebyshev polynomials of the first kind are nonnegative for &1 x 1, thereby generalising a well-known property of the original Hermite Feje r interpolation method. As an application of