论文信息 - The Bernstein Constant and Polynomial Interpolation at the Chebyshev Nodes

The Bernstein Constant and Polynomial Interpolation at the Chebyshev Nodes

In this paper, we establish new asymptotic relations for the errors of approximation in Lp?1,1], 00, by the Lagrange interpolation polynomials at the Chebyshev nodes of the first and second kind. As a corollary, we show that the Bernstein constantB?,p?limn?∞n?+1/p infck??x????k=0nmckxk?Lp?1,1] is finite for ?>0 and p?13,∞).

Michael I. Ganzburg

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