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Theodore A. Kilgore,<ref>{{cite journal |doi=10.1016/0021-9045(78)90013-8 |first=T. A. |last=Kilgore |title=A characterization of the Lagrange interpolating projection with minimal Tchebycheff norm |journal=J. Approx. Theory |volume=24 |issue= |pages=273 |year=1978 }}</ref> Carl de Boor, and Allan Pinkus<ref>{{cite journal |doi=10.1016/0021-9045(78)90014-X |first=C. |last=de Boor |first2=A. |last2=Pinkus |title=Proof of the conjectures of Bernstein and Erdös concerning the optimal nodes for polynomial interpolation |journal=[[Journal of Approximation Theory]] |volume=24 |issue= |pages=289 |year=1978 }}</ref> proved that there exists a unique ''t''<sub>''i''</sub> for each ''L''<sub>''n''</sub>, although not known explicitly for (ordinary) polynomials. Similarly, <math>\underline{\Lambda}_n(T) = \min_{-1 \le x \le 1} \lambda_n(T; x)</math>, and the optimality of a choice of nodes can be expressed as <math>\overline{\Lambda}_n - \underline{\Lambda}_n \ge 0.</math>
For Chebyshev nodes, which provides a suboptimal, but analytically explicit choice, the asymptotic behavior is known as<ref>{{cite journal |first=F. W. |last=Luttmann |first2=T. J. |last2=Rivlin |title=Some numerical experiments in the theory of polynomial interpolation |journal=IBM J. Res.
:<math>\overline{\Lambda}_n(T) = \frac{2}{\pi} \log(n + 1) + \frac{2}{\pi}\left(\gamma + \log\frac{8}{\pi}\right) + \alpha_{n + 1}</math>
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