摘要
设f(x)∈C^k[0,1],k=2,3;又令H_3(x)是满足条件H_3(0)=f(0),H_3(1)=f(1),H_3~"(0)=f"(0)及H_3"(1)=f"(1)的三次HB插值多项式,本文给出e^(α)(x)=H^(α)-f^(α)(x),α=0,1,2,k用‖f^(k)‖=max 0≤x≤1 |f^(k)(x)|来表示的最优误差界。
Let f(x)∈C^k[0, 1], k=2, 3 be given; let H_3(x) be the cubic HB inter-polation polynomial satisfying conditions H_3(0)=f(0), H_3(1)=f(1), H_3″(0)=f′(0) and H_3″(1) =f″(1). In this paper we obtain the optimal error boands fore^(α)(x)=H_3^(α)(x)-f^(α)(x), α=0,1,2,k in terms of ‖f^(k)‖=max 0≤x≤1 |f^(k)(x)|.
