Jeff Ledford, Luke Paris, Ryan Urban, Alec Vidanes
This note concerns the interpolation problem with two parametrized families of splines related to polynomial spline interpolation. The authors address the questions of uniqueness and establish basic convergence rates for splines of the form \(s_\alpha=p \cosh (\alpha \cdot)+q \sinh (\alpha \cdot)\) and \(t_\alpha=p+q \tanh (\alpha \cdot)\) between the nodes where \(p, q \in \Pi_{k-1}\).