We're trying to approximate the Runge function $f(x) = \dfrac{1}{1+25x^2}$ using Chebyshev nodes. When calculating the interpolation error, using different degrees ranging from 0 to 50, we get the following plot:

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The blue dots are the interpolation errors using Chebyshev points for increasing degrees. We use a logaritmic scale for the vertical axis. As you can clearly see, they oscillate quite a bit. This oscillating seems to depend on the degree: if it's even, the errors are a bit lower.

Using equidistant points, we get exactly the same but if the degree is even, the errors are a bit higher.

What is a possible explanation for this phenomenon?



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