Ck连续的保形分段2k次多项式插值

This paper describes a method for shape preserving smooth piecewise polynomial S(x) of degree 2k which passes through a given set of data points {x1, yi}i=0 n+1 (xi＜xi+1 , i =1, 2,…, n + 1). If we give the first derivative of curve at each data point, then in data interval [xi, xi+1] a necessary and sufficient conditions is derived for the convexity preserving of interpolation polynomial of degree 2k. By inserting at most one internal knot at each data interval, a Ck shape preserving piecewise interpolating polynomial of Degree 2k is obtaind. At fat a few data examples illustrate the method is correct and effective.