[gp7]

This page crashes my chrome tab!!

Anyway, anyone interested enough in this to be reading this comment thread should go look up approximation theory and approximation practice by trefethen [0], which is a very very good book, that covers chebyshev polynomials in a very clear way. The real party trick you get out of it, though, is that by taking samples of functions at the roots of chebyshev basis polynomials and applying the discrete cosine transform, you can get a set of chebyshev coefficients to approximate a function in O(n log n) time

[0] https://people.maths.ox.ac.uk/trefethen/ATAP/

[m_myers]

> This page crashes my chrome tab!!

The problem appears to be the SVG image http://mooooo.ooo/chebyshev-sine-approximation/horner_ulp.sv..., which has a path of 5000+ points.

[wallacoloo]

Ah, my bad. I thought browser support for SVGs was pretty robust at this point. I've gone ahead and rasterized all the images (save for the inline equations), but clicking on the images will still take you to the original SVGs.

[tanderson92]

I've always found DCTs and particularly Clenshaw-Curtis quadrature (better than Gauss quadrature arguably!) attractive: you can do an incredible amount of heavy lifting with this corner of approximation theory.