I have to find an approximate continuous function that passes through a number of points. Many have said that the best (for my specific problem) is to use Chebyshev polynomial decomposition. I have another solution and I want to know if there is any real differences in the precision (or something else) between these two strategies:
1-I can have a Lagrange interpolation polynomial on Chebyshev extrema points.
2-I can have a Chebyshev decomposition on its extrema points.
We know that both of them are polynomials of the same order, both uses the same points, and both polynomials pass exactly through these points. As there is one unique polynomial of such type, is there any differences between these two approximations?