Mathematics Colloquium

Tel Aviv University

Monday, November 6, 2017
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.

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