A Generalized Asymptotic Upper Bound on Fast Polynomial Evaluation and Interpolation
A Generalized Asymptotic Upper Bound on Fast Polynomial Evaluation and Interpolation
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快速多项式求值和插值的广义渐近上界
DOI：
10.1137/0205047
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发表时间：
1976
期刊：
影响因子：
--
通讯作者：
F. Chin
中科院分区：
文献类型：
--
作者：
F. Chin
本文显示的是，评估和插值问题对应于一组点，$ \ {x_i \} _ {i = 0}^{n -1} $，带有$（C_I-1）$较高的衍生物每个$ x_i $，以便$ \ sum _ {i = 1}^{n -1} c_i = n $，可以在$ o（[n \ log n] [（\ log n） + 1]）$ steps.l此上限与两个极端情况的已知上限完美匹配，即$ o（n \ log ^2 n ）$和$ o（n \ log n）$ steps $ n = n $和$ n = 1 $时。
It is shown in this paper that the evaluation and interpolation problems corresponding to a set of points, $\{ x_i \} _{i = 0}^{n - 1} $, with $(c_i - 1)$ higher derivatives at each $x_i $ such that $\sum _{i = 1}^{n - 1} c_i = N$, can be solved in $O([N\log N][(\log n) + 1])$ steps.l This upper bound matches perfectly with the known upper bounds of the two extreme cases, which are $O(N\log ^2 N)$ and $O(N\log N)$ steps when $n = N$ and $n = 1$, respectively.