LAUSR

We consider the problem of Subbotin’s parabolic spline interpolation for functions with large gradient domains. In the case of the common piecewise uniform Shishkin’s mesh we obtain two-sided accuracy estimates for the class of functions with exponential boundary layer. The spline interpolation accuracy estimates are not uniform in a small parameter, while the error itself can grow unboundedly as the small parameter vanishes and the number N of nodes remains fixed. We include the results of some simulations.