Optimal parameter choice for a class of cubic interpolation kernels and the associated error analysis

Two issues related to a class of cubic kernels for interpolation with a single free parameter are addressed in this paper. The first issue relates to parametrizing the cubic interpolation kernel optimally for arbitrary kernel length keeping in view the need to cancel all error terms up to the second order. This builds upon the results of Keys (1981) where the optimal parameter value is obtained only for a kernel length of 2. The second issue relates to obtaining a precise mathematical formulation for the advantage gained in increasing the kernel length. The associated third order error analysis shows that the error coefficients decrease monotonically in magnitude with an increase in the kernel length. Asymptotic results are also obtained for the spline length tending to infinity.