Constructive methods in convex \(C^ 2\) interpolation using quartic splines
This paper is concerned with a method for convexity preserving \(C^2\) interpolation which uses quartic splines on refined grids and is successful for all strictly convex data sets. The original grid is refined with one additional knot in each subinterval. These added knots are chosen in order to retain the desired convexity. The authors propose several explicit algorithms and two methods for the placement of the knots. Since the interpolants are not uniquely determined, a positive definite quadratic optimization problem has to be solved. Some results of numerical experiments are reported and discussed.
scientific article; zbMATH DE number 915386