The Bernstein Constant and Polynomial Interpolation at the Chebyshev Nodes
نویسندگان
چکیده
منابع مشابه
Multivariate polynomial interpolation on Lissajous-Chebyshev nodes
In this contribution, we study multivariate polynomial interpolation and quadrature rules on non-tensor product node sets linked to Lissajous curves and Chebyshev varieties. After classifying multivariate Lissajous curves and the interpolation nodes related to these curves, we derive a discrete orthogonality structure on these node sets. Using this discrete orthogonality structure, we can deriv...
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Interpolation polynomial pn at the Chebyshev nodes cosπj/n (0 ≤ j ≤ n) for smooth functions is known to converge fast as n → ∞. The sequence {pn} is constructed recursively and efficiently in O(n log2 n) flops for each pn by using the FFT, where n is increased geometrically, n = 2i (i = 2, 3, . . . ), until an estimated error is within a given tolerance of ε. This sequence {2j}, however, grows ...
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It is the purpose of this note to complete and extend the work of Kilgore [8] on the optimal nodes in polynomial interpolation. The problem is as follows. Consider the Banach space C[a, b] of continuous functions on the finite interval [a, b], with the usual norm lI,fi~ := max l.f'(x)l. nkxZ:h Throughout the paper, we take n to be a fixed integer, n 3 2. Corresponding to each point t in we cons...
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ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 2002
ISSN: 0021-9045
DOI: 10.1006/jath.2002.3729