Monday, November 6, 2017

12:15–13:10

Schreiber 006

12:15–13:10

Schreiber 006

Arieh Iserles

University of Cambridge

Approximation of wave packets on the real line

Motivated by the computation of quantum problems in semiclassical regime, we explore fast approximation of functions on the real line, in particular of wave packets – by "fast" we mean both rapid speed of convergence and the derivation of the first *n* expansion coefficients in O(*n* log *n*) operations. Specifically, we need to construct an orthogonal system in L(-∞,∞) with these welcome features and we explore four candidates: Hermite polynomials, Hermite functions, stretched Fourier functions and stretched Chebyshev polynomials. We analyse their speed of convergence, describe some unexpected phenomena and, using a panoply of techniques, determine the surprising winner.