摘要
Lagrange算子与Bernstein算子是用于处理多项式逼近问题的两个重要算子,这两种算子各有优缺点.为此,Sablonniere P.引入并研究了一种新的算子B(nk),它是一种介于Lagrange算子与Bernstein算子之间的拟插值算子.笔者研究了如何利用这种算子来完成满足某些给定条件的多项式曲线的设计.由于最适合应用的多项式是三次多项式,研究B(3k)(k=0,1,2,3)的性质,此时,算子B(30)、B(31)是Bernstein算子B3,B(33)是Lagrange算子L3,且B(32)f≠B3f,B(32)f≠L3f,B(32)f在体现逼近效果以及f的性质方面表现是最好的,且B(32)f型多项式曲线可以通过基变换方法得到新的控制点再由Bezier曲线作图法做出.
Lagrange operator and Bernstein operator are two important operators which are used to deal with polynomial approximation problems. They have advantages and disadvantages of their own. Therefore, Sablonniere P. introduced and studied new operators Bn^（k）, which are quasi-interpolation operators between Lagrange operator and Bernstein operator. This paper studies how to make use of these operators to conduct a design of polynomial curve to satisfy certain given conditions. Because third-order polynomials are the most proper for applicatoin, this paper studies the properties of B3^（k） （k =0,1,2,3）. Here B3^（0） and B3^（1） are Bernstein operator,B3 and B3^（3） are Lagrange operator L3, but B3^（2）f≠B3f,B3^（2）f≠L3f. B3^（2）f is the best in embodying approximation effect and the property of f, and new control points can be obtained through basis changing. Then a B3^（2）f type polynomial curve can be drawn by the Bezier curve graph drawing method.
出处
《辽宁师范大学学报（自然科学版）》
CAS
北大核心
2006年第3期260-263,共4页
Journal of Liaoning Normal University:Natural Science Edition
