Rational spline histopolation of convex data

The histopolation with quadratic/linear rational splines of class C-2 is studied. These splines keep the sign of its second derivative on the whole interval and because of that the given histogram is assumed to be strictly convex. The grid points of the histogram and spline knots between them are supposed to be placed arbitrarily. We show that there is a strictly convex histogram without the solution of histopolation problem for any choice of spline knots. Presented numerical examples illustrate this result. (C) 2020 Published by Elsevier B.V. on behalf of IMACS.