(section-globalapprox-next)=
# Next steps

The topics in this chapter come mainly under the heading of *approximation theory*, on which there are many good references. A thorough introduction to polynomial interpolation and approximation, emphasizing the complex plane and going well beyond the basics given here, is {cite}`trefethenApproximationTheory2013`. A more thorough treatment of the least-squares case is given in {cite}`davisInterpolationApproximation1963`.

A thorough comparison of Clenshaw–Curtis and Gauss–Legendre integration is given in {cite}`trefethenGaussQuadrature2008`.

The literature on the FFT is vast; a good place to start is with the brief and clear original paper by Cooley and Tukey {cite}`cooleyAlgorithmMachine1965`. A historical perspective by Cooley on the acceptance and spread of the method can be found at the SIAM History Project at http://history.siam.org/cooley.htm (reprinted from Nash {cite}`nashHistoryScientific1990`).  The FFT has a long and interesting history.

Doubly exponential integration, by contrast, is not often included in books. The original idea is presented in the readable paper {cite}`takahasiDoubleExponential1973`, and the method is compared to Gaussian quadrature in {cite}`baileyComparisonThree2005`, which is the source of some of the integration exercises in {numref}`section-globalapprox-improper`.