摘要
讨论了混合型Ｊａｃｏｂｉ节点的Ｌａｇｒａｎｇｅ插值多项式的二阶导数对函数的二阶导数的逼近
The following theorem is given: Theorem Suppose f(x)∈C 2 . Let L n(f;x) n(f; x) be Lagrange′s interpolation polynomials based on “mixed” Jacobi′s nodes:x k= cos 2kπ2n+1 , k=1,2,…,n(nodes: k= cos 2k-12n+1π) . Then we have |L″ n(f;x)-f″(x)|≤A n(x)E n-3 (f″)and |L″ n(f;x)-f″(x)|≤B n(x)E n-3 (f″) ,whereA n(x)=K ln n(1-x) 2{n1-x+1n1-x} , 0≤x<1, K ln n1+x{n+11+x} , -1<x≤0 . B n(x)=K ln n1-x{n+11-x} , 0≤x<1, K ln n(1+x) 2{n1+x+1n1+x} , -1<x≤0 . and E n(f″) is the best approximation of f″(x) by polynomials of degree ≤ n .
出处
《纯粹数学与应用数学》
CSCD
1997年第1期84-89,共6页
Pure and Applied Mathematics
基金
山东省自然科学基金
