等距节点上(0,3)插值五次样条

§1.引言 设f(x)是定义在0,1]上的连续函数,n是自然数。记h=1/n, f_v~((r))=f~((r))(vh),v=0,1,…,n;r=0,1,…,5, f_(v 1/2)~((r))=f~((r))((v 1/2)h),v=0,1,…,n-1;r=0,1,…,5, ω_r(j)=max |f~((r))(x_1)-f~((r))(x_2)|,r=0,1,…,6. |x_1-x_2|≤h 0≤x_1,x_2≤1又设s(x)是0,1]上满足(i)s(x)∈C~30,1],(ii)在vh,(v 1)h]上s(x)∈∏_5,v=0,1,…,n-1的五次样条.它们的全体记为?_(n5)~((3)) .

(0,3) QUINTIC LACUNARY INTERPOLATION SPLINES

In this paper, another kind of quintic lacunary interpolation splines which inter-polate to (0, 3), date on equidistant knots are. discussed. Theorems of existence, uni-queness and estimates of rate of convergence are established.