Comonotone Adaptive Interpolating Splines

For any given data we propose the construction of an interpolating spline of class C1, which is either a quadratic polynomial or a linear/linear rational function between the knots, and preserves the monotonicity of the data on the sections of rational intervals. We prove the uniqueness and existence of this spline. Numerical tests show good approximation properties and flexibility due to the non-coincidence of the given data arguments and the spline knots which can be chosen freely.