摘要
研究插值多项式对|x|α达到最佳逼近度的一种构造方法,证明了当n=2m,m∈N,α∈(0,1]时,Fn(α)<2231-αnα,其中F2m(α)=max-1≤x≤1||x|α-R2m(x)|,R2m(x)是以x0=0,xj=cosj-12π2m(j=1,2,…,2m)为插值结点的对|x|α的Lagrange插值多项式,从而推广了M.Revers的结论.
The approximation to function |x|~α by interpolation polynomials by which the best approxiamtion order is achieved is considered, it is showed that: for n=2m, m∈N, α∈(0,1],F_n(α)<223^(1-α)n~α,where F_(2m)(α)=(max)-1≤x≤1||x|~α-R_(2m)(x)|,R_(2m)(x) is the Lagrange interplation polynomial to |x|~α based on the Chebyshev nodes: x_0=0,x_j= cos j-12π2m(j=1,2,…,2m), the corresponding result obtained by M. Revers is then extended.
出处
《浙江大学学报（理学版）》
CAS
CSCD
2004年第1期21-23,共3页
Journal of Zhejiang University（Science Edition）
基金
国家自然科学基金资助项目(10141001)
浙江省自然科学基金资助项目(100042).
