>This blog post’s statement that “higher degree polynomials can have problems with numerical accuracy” turns out to be a myth (author here) I should have quali

>This blog post’s statement that “higher degree polynomials can have problems with numerical accuracy” turns out to be a myth (author here) I should have qualified or corrected that statement in my article. There are a few reasons I rarely use n>5: - when polynomial approximation is appropriate, high-degree polynomials are usually unnecessary on embedded systems (0.1% accuracy usually sufficient) - it's usually a sign that polynomial approximation is being misapplied and there are better ways (via range reduction, transformation like 1/f(x), etc.) - with least-squares, computation of the coefficients can have problems with numerical accuracy. When I've used least-squares fitting polynomials with n>10, I often get a complaint from my numerical tool (MATLAB or Python) that the matrix in question is ill-conditioned. That may be because I used the Vandermonde matrix rather than Chebyshev polynomials, or because I used a large number of points. Chebyshev approximation doesn't have the same problem, I don't think, and I should not have mapped my experience with least-squares fitting onto Chebyshev approximation. Evaluation of the polynomials themselves should be fine (after all, we can easily compute a 20th-degree Chebyshev polynomial).