Approximation by shape preserving interpolation splines (Q5937471)

The authors present a shape preserving method for interpolation of scattered data under some constraints such as convexity, monotonicity and positivity. The \(k\)-convex interpolation spline in Sobolev space is introduced. The shape preserving condition here is the positivity of the \(k\)-th derivative. An algorithm for computing the resulting function is given. Some convergence theorems are established.