First applications of a formula for the error of finite sinc interpolation

In former articles we have given a formula for the error committed when interpolating a several times differentiable function by the sinc interpolant on a fixed finite interval. In the present workwe demonstrate the relevance of the formula through several applications: correction of the interpolant through the insertion of derivatives to increase its order of convergence, improvement of the barycentric formula, rational sinc interpolants (with and without replacement of the (usually unknown) derivatives with finite differences), convergence acceleration through extrapolation and improvement of one-sided interpolants. Mathematics Subject Classification (2000) Primary 65D05 · 41A80; Secondary 65B05 · 65B15