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Approximation by polynomials with locally geometric rates

Authors: K. G. Ivanov, E. B. Saff and V. Totik
Journal: Proc. Amer. Math. Soc. 106 (1989), 153-161
MSC: Primary 41A25
MathSciNet review: 964456
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Abstract: In contrast to the behavior of best uniform polynomial approximants on $ [0,1]$ we show that if $ f \in C[0,1]$ there exists a sequence of polynomials $ \{ {P_n}\} $ of respective degree $ \leq n$ which converges uniformly to $ f$ on $ [0,1]$ and geometrically fast at each point of $ [0,1]$ where $ f$ is analytic. Moreover we describe the best possible rates of convergence at all regular points for such a sequence.

References [Enhancements On Off] (What's this?)

  • [1] K. G. Ivanov and V. Totik, Fast decreasing polynomials, Constr. Approx., 5 (1989). MR 1027506 (90k:26023)
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Keywords: Algebraic polynomials, approximation of functions, rate of decrease
Article copyright: © Copyright 1989 American Mathematical Society

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