Let ,: (& , ) Ä (0, ) be a given continuous even function and let m be a positive integer. We show that, with some additional restrictions on ,, there exist decreasing sequences x 1 , ..., x m and y 1 , ..., y m&1 of symmetrically located points on (& , ) and corresponding polynomials P and Q of deg
✦ LIBER ✦
Where Are the Nodes of “Good” Interpolation Polynomials on the Real Line?
✍ Scribed by J. Szabados
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 78 KB
- Volume
- 103
- Category
- Article
- ISSN
- 0021-9045
No coin nor oath required. For personal study only.
✦ Synopsis
It is shown that the interval where the nodes of a ``good'' interpolation polynomial are situated is strongly connected with the Mhaskar Rahmanov Saff number. 2000 Academic Press * n (x)=w(x) :
n k=0 |l k (x)| w(x k ) ,
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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