How to find Chebyshev nodes

Question

I want to use Chebyshev interpolation. But I am a little confused for finding Chebyshev nodes. I use the following figure to illustrate my problem. Consider I have a vector of numbers I depicted as a line In "A". In "B", the red points are the chebyshev nodes. How can i choose these points? (I have used the picture to say that I know that Chebyshev try to choose more points at the ends)

Answer 1

Chebyshev nodes are the roots of chebyshev polynomials. Use the definition $$T_n(x) = \cos(n\arccos(x))$$ for the Chebyshev polynomials.

Answer 2

For $n\;$ nodes $x_k\;$ in an interval $[a,b]\;$ other than $[-1,1]\;$ use the formula from http://en.wikipedia.org/wiki/Chebyshev_nodes: $$x_k = \frac{1}{2}(a+b) +\frac{1}{2}(b-a) \cos\left(\frac{2k-1}{2n}\pi\right), \quad k=1\dots n$$