A Fast Chebyshev-Legendre Transform via Toeplitz-Hankel Structure

Abstract: 

Chebyshev technology is frequently used for approximation of functions, but there are some situations in which an expansion in Legendre polynomials is advantageous. In this talk I will discuss a new fast transform method for converting between Chebyshev and Legendre coefficients by exploiting the Toeplitz-Hankel structure of the associated matrix and low-rank approximations. If time permits I will discuss how the approach generalises to other classical orthogonal polynomials. This is joint work with Alex Townsend (MIT) and Sheehan Olver (Sydney).