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Chebyshev Nodes for Interpolation

gucci

New member
Sep 1, 2013
13
Hello all,

I'm not sure if this is the right sub-forum for this question, so please move my post if there is a better place for this.

I have been studying interpolation of functions, and in particular, using Chebyshev nodes rather than equidistant points in the creation of an approximation polynomial. In my textbook, it states that "it is not difficult to construct examples where Chebyshev interpolation would not do well." However, I am having considerable difficulty coming up with an example on my own.

I understand that in the Runge function, the reason that Chebyshev nodes do a better job than equidistant points is that $\frac{f^{(n+1)}}{(n+1)!}$ grows near the endpoints of the interval [-1,1], and this happens to be where the Chebyshev nodes are more concentrated. But I don't know how to create an example where this is not the case.

I hope that this question makes sense, and I will be happy to explain further if something is unclear. Thank you in advance for any help you can offer,

gucci