On the numerical stability of the second barycentric formula for trigonometric interpolation in shifted equispaced points

We consider the numerical stability of the second barycentric formula for evaluation at points in $[0, 2\pi]$ of trigonometric interpolants in an odd number of equispaced points in that interval. We show that, contrary to the prevailing view, which claims that this formula is always stable, it actually possesses a subtle instability that seems not to have been noticed before. This instability can ...