Sufficient conditions for the comonotone interpolation of cubic C 2-splines

We consider the problem of interpolation of a function under the condition of the preservation of the nature of its piecewise monotonicity. We give sufficient conditions for the comonotone interpolation by a classical cubic C ²-spline in the representation based on the expansion of its first derivative in a basis consisting of B-splines. These conditions allow to determine whether the soobtained spline is comonotone without solving the interpolation problem.