Range restricted interpolation using Gregory's rational cubic splines

摘要

The construction of range restricted univariate and bivariate interpolants to gridded data is considered. We apply Gregory's rational cubic C1 splines as well as related rational quintic C2 splines. Assume that the lower and upper obstacles are compatible with the data set. Then the tension parameters occurring in the mentioned spline classes can be always determined in such a way that range restricted interpolation is successful.