Hermite样条插值余项的精确估计—关于Lipow和Schoenberg的猜测

Hermite样条插值余项的精确估计—关于Lipow和Schoenberg的猜测 EXACT ESTIMATES OF REMAINDERS OF HERMITE INTERPOLATING SPLINES——ON CONJECTURE OF LIPOW AND SCHOENBERG 王建忠 Wang Jianzhong first-author Lipow和Schoenberg在1973年曾讨论了基Hermite插值问题。他们给出了插值的Lagrange-Hermite公式,但是关于插值误差没有完整的结果,只是提出了一个猜测。本文对插值误差作了较仔细的分析,得到了误差的精确估计,也证实了他们猜测的正确性。 In[1], （see Lipow and Schoenberg in Linear algebra and its applications. 6（1973）273-304） Lipow and Schoenbetg discussed the cardinal Hermite interpolation problem. After giving the so-called Lagrange-Hermite formula: f（x）= f（v）L 0 （x-v）+…+ f（r-1）（v）L r-1 （x-v）+R（x）, they expect a discussion of the remainder R（x）, and guess, for increasing r, the remainder to be tapering off as r appaaches m. In this paper we abtain the exact estimates of the remainders R（x） for all r, 1≤r≤m, and verify their guess. 1985-04-01 2021-04-01 4