Lagrange interpolation on generalized Jacobi zeros with additional nodes
β Scribed by G. Criscuolo; G. Mastroianni
- Publisher
- Akadmiai Kiad
- Year
- 1994
- Tongue
- English
- Weight
- 857 KB
- Volume
- 65
- Category
- Article
- ISSN
- 1588-2632
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π SIMILAR VOLUMES
Necessary and sufficient conditions are obtained for a continuous function guaranteeing the uniform convergence on the whole interval [ &1, 1] of its Lagrange interpolant based on the Jacobi nodes. The conditions are in terms of 4-variation, 8-variation, the modulus of variation, and the Banach indi
## Abstract Weighted __L^p^__ convergence of derivatives of extended Lagrange interpolation at the union of zeros of generalized Jacobi polynomials and some additional points is investigated.
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
We consider the ``Freud weight'' W 2 Q (x)=exp( &Q(x)). let 1<p< , and let L\* n ( f ) be a modified Lagrange interpolation polynomial to a measurable , where 2 is a constant depending on p and :.