THE CONVEX INTERPOLATION OF HISTOGRAM BY POLYNOMIAL SPLINES

Pavel Ženčák

   This paper treats the interpolation of a convex histogram by strictly convex polynomial splines of arbitrary degree. First, the existence theorem for strictly convex spline solving some special interpolation problem is proved using the B-spline representation. Next, the general existence theorem for strictly convex splines of order k interpolating convex histogram on (k .. 1) -fold refined mesh is presented. Finally, the numerical algorithm for computing such spline is shown.

Keywords: Strict convexity, polynomial splines, interpolation, histogram

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