摘要
微分插值公式f(x)=H_(n)(x)+R_(n)(x)(1)导出数值微分公式f^((k))(x)=H_(n)^((k))(x)+Rn^((k))(x)(o≤k≤n),(2)这里H_(n)(x)为函数f(x)的n次插值多项式。
Let H_(n)(x)be the interpolation polynomial of degree n for a function f(x).The kth(k=0,1,…,n)derivatives R_(n)^((k))(x)of R_(n)(x)=f(x)-H_(n)(x)have been represented here in formula(4)or(4′)by divided differences or derivatives of orders n+1,n+2,…,n+m+1 of f(x),where m=0,1,…,k can even be arbitrarily chosen.In some particular cases,formtfla(4′)can give the Lagrangian type representation,if we take m=0 or 1.
出处
《科学通报》
1979年第19期869-872,共4页
Chinese Science Bulletin
