Hermite Interpolation in the Roots of Unity

✍ Scribed by T.N.T. Goodman; K.G. Ivanov; A. Sharma

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 621 KB
• Volume: 84
• Category: Article
• ISSN: 0021-9045
• DOI: 10.1006/jath.1996.0004

✦ Synopsis

We study the polynomial H r, n ( f, z) which interpolates an analytic function f and its derivatives up to order r&1 at the n th roots of unity. In particular we relate the vanishing of the coefficients of the highest powers of z in the Hermite interpolant H r, n ( f, z) with the vanishing at certain points of the Hermite interpolants of certain functions related to f.