Tuesday,
February 23, 12:00 p.m. ECG 317
Rodrigo Platte
School of Math&Stats
Impossibility of Approximating Analytic Functions from
Equispaced Samples at Geometric Convergence Rates
Abstract
How fast can one recover an analytic function from equally spaced
samples? For periodic functions, for instance, one can obtain geometric
convergence rates as the number of samples is increased using Fourier
expansion. In general however, we show that such fast rates are not
possible without compromising stability. More specifically, it is shown
that no stable procedure for approximating functions from equally spaced
samples can converge geometrically for analytic functions. This work is
in collaboration with L.N. Trefethen and A.B. Kuijlaars.
