Best uniform rational approximation of $x^\alpha$ on $[0,1]$
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- by Herbert Stahl PDF
- Bull. Amer. Math. Soc. 28 (1993), 116-122 Request permission
Abstract:
A strong error estimate for the uniform rational approximation of ${x^{\alpha }}$ on [0, 1] is given, and its proof is sketched. Let ${E_{nn}}({x^\alpha },[0,1])$ denote the minimal approximation error in the uniform norm. Then it is shown that \[ \lim \limits _{x \to \infty } {e^{2\pi \sqrt {\alpha n} }}{E_{nn}}({x^\alpha },[0,1]) = {4^{1 + \alpha }}|\sin \pi \alpha |\] holds true for each ${\alpha > 0}$.References
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Additional Information
- © Copyright 1993 American Mathematical Society
- Journal: Bull. Amer. Math. Soc. 28 (1993), 116-122
- MSC: Primary 41A20
- DOI: https://doi.org/10.1090/S0273-0979-1993-00351-3
- MathSciNet review: 1168517