-[Chebyshev polynomials](https://en.wikipedia.org/wiki/Chebyshev_polynomials) are simply a well-behaved basis for polynomial functions in a given finite interval, so you can view FastChebInterp as a robust and convenient way to do perform multidimensional polynomial fitting and interpolation. Fitting to high-degree polynomials can be problematic unless your number of data points is much greater than the product of the polynomial degrees (the number of polynomial terms), but if you have a [smooth function](https://en.wikipedia.org/wiki/Smoothness) and interpolate from specially chosen points — the Chebyshev points, given by the function `chebpoints` below — then it is very well behaved, and in fact converges exponentially fast for analytic functions. (See, for example, the book [*Approximation Theory and Approximation Practice*](https://www.chebfun.org/ATAP/) by Trefethen.)
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