9.8. 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 [Tre13]. A more thorough treatment of the least-squares case is given in [Dav63].
A thorough comparison of Clenshaw–Curtis and Gauss–Legendre integration is given in [Tre08].
The literature on the FFT is vast; a good place to start is with the brief and clear original paper by Cooley and Tukey [CT65]. 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 [Nas90]). 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 [TM73], and the method is compared to Gaussian quadrature in [BJL05], which is the source of some of the integration exercises in Section 9.7.