  This note concerns the finite interpolation problem with two parametrized
families of splines related to polynomial spline interpolation. We 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 $p,q\in\Pi_{k-1}$.
