Let's say the n-degree Chebyshev polynomials :
$$ T_{n} (x)=\cos(n\arccos(x))$$
Make a polynomial such that:
$$\mid y- P (x) \mid$$
be minimal, using the first three Chebyshev polynomials for the following data:
\begin{bmatrix} x & -1 & -0.5 & 0 & 0.5 & 1 \\ y & 0.6346 & 0.6565 & 1 & 1.5230 & 1.5756 \end{bmatrix}
How could we manage to approach such a problem?