C^k连续的保形2k＋1次分段多项式插值

C￣k SHAPE PRESERVING PIECEWISE POLYNOMIAL OF DEGREE 2k+1 INTERPOLATION

Ｃ￣ｋ连续的保形２ｋ＋１次分段多项式插值方逵，朱国庆，周经伦（国防科学技术大学数学系）Ｃ￣ｋＳＨＡＰＥＰＲＥＳＥＲＶＩＮＧＰＩＥＣＥＷＩＳＥＰＯＬＹＮＯＭＩＡＬＯＦＤＥＧＲＥＥ２ｋ＋１ＩＮＴＥＲＰＯＬＡＴＩＯＮ￥ＦａｎｇＫｕｉ；ＺｈｕＧｕｏ－ｑｉｎｇ...

AbstractThis paper describes a method for shape-preserving smooth piecewise polynomial of degree 2k+1 through a given set of data points {xi, yi}=0, xi<xi+1, i= 1, 2,…) n-1. If we give the first derivative of curve at each data point, then in each data interval [xi, xi+1] we derive the necessary and sufficient conditions of convexity-preserving of interpolation polynomial of degree 2k+1. We construct Ck shape-preserving piecewise polynomial of degree 2k+1 interpolates by inserting at most one internal knot at each data interval. At last a few data examples illustrate that our method is correct and effective.