CAM Colloquium - Alex Townsend: Fast transforms based on asymptotic expansions of special functions

A great success of the 20th century was the development of fast transforms such as the fast Fourier transform, the fast multipole method, and butterfly algorithms. In this talk we carefully employ asymptotic expansions of special functions to develop a new family of fast transforms with rigorous a priori error bounds and essentially no initialization cost. Applications so far include fast L2 projection with the Legendre basis, analysis of the cosmic microwave background, and the mollification of rough acoustic media.