## Abstract We recognize that established techniques permit twoβdimensional interpolation to be accomplished efficiently as well as accurately when the grid of points, on which the data is available, is regular. Existing methods suitable for irregular grids are computationally protracted. We show t
Lagrange Interpolation on Chebyshev Points of Two Variables
β Scribed by Yuan Xu
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 756 KB
- Volume
- 87
- Category
- Article
- ISSN
- 0021-9045
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β¦ Synopsis
We study interpolation polynomials based on the points in [&1, 1]_[&1, 1] that are common zeros of quasi-orthogonal Chebyshev polynomials and nodes of near minimal degree cubature formula. With the help of the cubature formula we establish the mean convergence of the interpolation polynomials.
π SIMILAR VOLUMES
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
Polynomial interpolation of two variables based on points that are located on multiple circles is studied. First, the poisedness of a Birkhoff interpolation on points that are located on several concentric circles is established. Second, using a factorization method, the poisedness of a Hermite inte
Stable polynomial evaluation and interpolation at n Chebyshev or adjusted (expanded) Chebyshev points is performed using O(nlog' n) arithmetic operations, to be compared with customary algorithms either using on the order of n\* operations or being unstable. We also evaluate a polynomial of degree d
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