Fast Algorithms for Polynomial Interpolation, Integration and Differentiation.

摘要

For functions tabulated at Chebyshev nodes on an interval, spectral interpolation, integration and differentiation can be performed stably and efficiently via the fast Fourier transform. In this paper, a group of algorithms is presented for the efficient evaluation of Lagrange polynomial interpolants at multiple points on the line, and for the rapid spectral integration and differentiation of functions tabulated at nodes other than Chebyshev.