How does one evaluate a Chebyshev interpolant? One good approach, involving O(n log n) work for a single point evaluation, is to compute Chebyshev coefficients and use the Chebyshev series. However, there is a direct method requiring just O(n) work, not based on the series expansion, that is both elegant and numerically stable. It also has the advantage of generalizing to sets of points other than Chebyshev. It is called the barycentric interpolation formula, introduced by Salzer, with an earlier closely related formula due to Marcel Riesz.
