Talk:Chebyshev nodes

Indices in Interpolation Error

Shouldn't the indices in the formula for the interpolation error run from i = 1 up to i = n, since x_0 does not exist? The final expression for the interpolation error will then become

$\|f-p\|_{\infty }\leq {\frac {1}{2^{n-1}n!}}\max _{\xi \in [-1,1]}f^{(n)}(\xi )$

Could be I'm mistaken, though. 62.194.131.196 (talk) 21:28, 9 January 2009 (UTC)

The problem seems to be that the definition of n changes in the article. In the first section, Definition, the index runs from i = 1 to i = n, while in the second section the index starts at i = 0. That's confusing, and thus I rewrote the second section. It now arrives at the formula you quote. Many thanks for your comment. -- Jitse Niesen (talk) 22:49, 9 January 2009 (UTC)

Inconsistency of Ordering of Nodes

This edit changed the affine transformation so that the resultant nodes were ordered in ascending order, that is, the first node corresponds to the node closest to b, and the last corresponds to the node closest to a. However, this is inconsistent with the formula $x_{k}=\cos \left({\frac {2k-1}{2n}}\pi \right){\mbox{ , }}k=1,\ldots ,n.$ given in the previous section, which has the first node closest to the value 1 (corresponding to a), not -1 (corresponding to b). The order of the nodes doesn't particularly matter, but the two formulas should be made consistent. The sign of the cosine term in one equation should be changed. — Preceding unsigned comment added by 170.140.147.203 (talk) 18:12, 7 May 2014 (UTC)