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Trigonometric Interpolation and Quadrature in Perturbed Points


Sep 25, 2017 - 1:50pm to 2:55pm


Rettaliata Engineering Center, Room 104


Anthony Austin
Mathematics and Computer Science Division, Argonne National Laboratory


The trigonometric interpolants to a periodic function in equispaced grids converge if the function is Dini-continuous, and the associated quadrature rule, the trapezoid rule, converges if the function is continuous. We investigate the robustness of these results in the presence of perturbations to the grid points. We present theorems that quantify the effects of perturbing the points on the rates of convergence of both the approximation and quadrature schemes and explore connections with sampling theory, the Kadec 1/4 theorem, and the Fejér-Kalmár-Walsh theorem.

Event Type: 

Department of Applied Mathematics - Colloquia