Near-optimal tension parameters in convexity preserving interpolation by generalized cubic splines

We offer the algorithm for choosing tension parameters of the generalized splines for convexity preserving interpolation. The resulting spline minimally differs from the classical cubic spline and coincides with it if sufficient convexity conditions are satisfied for the last one. We consider specific algorithms for different generalized cubic splines such as rational, exponential, variable power, hyperbolic splines, and splines with additional knots.

Automated summary

The paper presents an algorithm for selecting tension parameters of generalized splines for convexity preserving interpolation. Specific algorithms for different generalized cubic splines are considered, including rational, exponential, variable power, hyperbolic splines, and splines with additional knots.