Convexity-preserving approximation by univariate cubic splines

A convexity-preserving approximation method is presented. Similar to the cubic spline interpolation, the given approximation function is univariate cubic spline with C2C2 continuity. A very simple computing method is described. The approximation order and polynomial reproducing property of this convexity-preserving approximant are discussed. The computing method for interpolating a small quantity of data is given. Some numerical examples are given to show the effectivity.