On Mean Convergence of Lagrange Interpolation for General Arrays
β Scribed by D.S. Lubinsky
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 91 KB
- Volume
- 104
- Category
- Article
- ISSN
- 0021-9045
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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
Weighted mean convergence of generalized Jacobi series is investigated, and the results are used to prove weighted mean convergence of various interpolating polynomials based on the zeros of generalized Jacobi polynomials. C 1993 Academic Press. Inc.
Weighted mean convergence of interpolating polynomials based on the zeros of generalized Jacobi polynomials is investigated. The approach is based on generalized Jacobi series and Marcinkiewicz-Zygmund type inequality. 1994 Academic Press. Inc.
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