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Proceedings of the American Mathematical Society

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Distribution of alternation points in uniform polynomial approximation

Author: G. G. Lorentz
Journal: Proc. Amer. Math. Soc. 92 (1984), 401-403
MSC: Primary 41A50; Secondary 41A10
MathSciNet review: 759662
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Abstract: For a continuous function $ f$ on $ \left[ {0,1} \right]$, we discuss the points where the polynomial $ {P_n}\left( x \right)$ of best uniform approximation deviates most from $ f\left( x \right)$, and the signs of the difference $ f\left( x \right) - {P_n}\left( x \right)$ alternate. We show that these points can be very irregularly distributed in $ \left[ {0,1} \right]$, even if $ f$ is entire.

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Article copyright: © Copyright 1984 American Mathematical Society