摘要
我们构造一个多项式p_(m.n),它既是对给定的函数f∈L_2[a,b]在给定的几个结点上的υ次插值,又是在同样性质的插值下次数小于等于m的多项式中到f的最佳逼近,并且当f∈C[a,b],m→∞是‖p_(m.n)-f‖L_2→0。
We construct the polynomial pm,n of degree m which interpolates a given function f∈Lω2[a,b] at pre-assigned n distinct nodes with multiplicity v and is the best approximation to f in the L2-sense over all polynomials of degree ≥m with the same in-terpolatory character. It is shown that the L2-error ||pm,n-f||L2→0 as m→0 if f∈c[a,b]
出处
《山西师大学报（自然科学版）》
1998年第4期7-10,共4页
Journal of Shanxi Teachers University(Natural Science Edition)
基金
辽宁省博士起动基金资助项目-971106
关键词
多重插值
L2逼近
最佳逼近
插值多项式
Interpolation Multiplicity orthogonal basis Least squares approximation uniformly dense
