Convex interval interpolation using a three-term staircase algorithm

Motivated by earlier considerations of interval interpolation problems as well as a particular application to the reconstruction of railway bridges, we deal with the problem of univariate convexity preserving interval interpolation. To allow convex interpolation, the given data intervals have to be in (strictly) convex position. This property is checked by applying an abstract three-term staircase algorithm, which is presented in this paper. Additionally, the algorithm provides strictly convex ordinates belonging to the data intervals. Therefore, the known methods in convex Lagrange interpolation can be used to obtain interval interpolants. In particular, we refer to methods based on polynomial splines defined on grids with additional knots. Received September 22, 1997 / Revised version received May 26, 1998