五次缺插值样条的渐近性态

f(x)定义于0,1]。将0,1]n等分,记x_j=jh,j=0,…,n.h=1/n,且 f~(α)(x_j)=f_j~(α),j=0,…,n;α=0,1,…,5。 A.Meir和A.Sharma提出五次缺插值样条函数,即满足下面条件的函数s_n(x): (i)s_n(x)∈C~30,1], (ii)在区间x_j,x_(j 1)]上(j=0,…,n-1),s_n(x)是五次多项式, (iii)s_n(x_j)=f_j,s″_n(x_j)=f″_j,j=0,…,n, (iv)s′_n(0)=f′_0,s′_n(1)=f′_n。 (1) 1]还考虑了把(1)中的(iv)换成 (iv′)s′′′_n(0)=f′′′_0,s′′′_n(1)=f′′′_n (2)的五次样条。为叙述方便,我们分别称之为(Ⅰ)型、(Ⅱ)型缺插值样条。1]证明了(Ⅰ),(Ⅱ)型插值样条在n为奇数时是唯一存在的。2,3,4]继续了这方面的工作,得到了一

THE ASYMPTOTIC EXPANSIONS OF QUINTIC LACUNARY INTERPOLATION SPLINES

The asymptotic expansions of quintic lacunary interpolation splines are obtained in thecase of uniform mesh. Hence the error bounds are estimated more accurately.