A KEEP-CONVEX INTERPOLATION FOR MONOTONIC SMOOTH FUNCTIONS
单调光滑函数的保凸插值方法

In this paper, a necessary and sufficient condition is obtained for the problemof monotonic spline interpolation with a quadratic spline solution. For the problem of monotonicfunction interpolation, we give a brief solution, i. e. a method of smoothing piecewise linearfunctions with integration. In addition we prove that the interpolation function given by thismethod not only is monotone smooth but also keeps the convexity of its values at the nodes.