| | | | | 关于Hermite插值余项的几点注记 | | | 周志强 | | | 研究Hermite插值余项E(x)=f(x)-H(x)=m1!f(m)(ξ)ωm(x).在一定条件下估计‖f(m)(x)‖∞和‖ωm(x)‖∞的上界.提出一种在给定精度ε下计算f(x)的算法,同时给出数值实验.
【作者单位】：怀化学院数学系 湖南怀化418008
【关键词】：Hermite插值;余项;计算量极小化
【基金】：湖南省教育厅科研基金资助项目(04C464).
【分类号】：O174.42
【DOI】：cnki:ISSN:1671-9743.0.2006-08-014
【正文快照】：
设f(x)∈Cn[a,b],f(n+1)(x)在(a,b)内存在,插值节点{xi}in=0及对应的函数值{fi}in=0,则插值多项式Ln(x)与f(x)的误差为E(x)=f(x)-Ln(x)=(n+11)!f(n+1)(ξ)ωn+1(x).本文讨论更一般的情形,即所谓Hermite插值余项,并估计其误差界.同时给出一种在给定精度ε下计算f(x*)的算法,该算法使计算量达到极小化.1Hermite插值余项估计设Hermite插值多项式Hn满足d0(Hn)≤m-1,(1)H(nk)(xi)=f(k)(xi),0≤i≤n,0≤k≤αi.(2)这里d0(Hn)表示多项式Hn(x)的次数,αi,i=0,1,…,n均为正整数,m=∑in=0(αi+1).定理1设f(x)∈Cm[a,b],Hn(x)由(1)(2)两式定义,E(… | | |  推荐 CAJ下载  PDF下载 | | | CAJViewer7.0阅读器支持所有CNKI文件格式，AdobeReader仅支持PDF格式 | | | | Some Results of Hermite Interpolation Remainder | | | ZHOU Zhi-qiang (Department of Mathematics;Huaihua University;Huaihua;Hunan 418008) | | | We consider n+1 distinct numbers x_0,x_1,…,x_m and the values of the function f and it's derivative f (k) (x_j) at these n+1 given points.We study the problem of estimating f(x) at a point x=x* ,within a given accuracy ε ,using Hermite polynomial interpolation.Based on the analysis of the Hermite interpolations and their erros,we present an algorithm which better exploits the results of the calculus,contributing to a decrease in the amount of work involved,respectively the computational cost neccessary to approximate f(x*) with a given error.The paper also gives numerical examples solved using this algorithm.
【Keyword】：Hermite interpolation;remainder of interpolation;minimizing computation |
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