The trigonometric interpolants to a periodic function f in equispaced points converge if f is Dini-continuous, and the associated quadrature formula, the trapezoidal rule, converges if f is continuous. What if the points are perturbed? Amazingly little has been done on this problem, or on its algebraic (i.e. nonperiodic) analogue. I will present new results joint with Anthony Austin which show some surprises.
- Numerical Analysis Group Internal Seminar