On the Number of Multiplications for the Evaluation of a Polynomial and Some of Its Derivatives
On the Number of Multiplications for the Evaluation of a Polynomial and Some of Its Derivatives
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关于多项式及其某些导数求值的乘法次数
DOI：
10.1145/321796.321810
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发表时间：
1974
期刊：
影响因子：
--
通讯作者：
Joseph F. Traub
中科院分区：
文献类型：
--
作者：
Mary Shaw;Joseph F. Traub
本文给出了求多项式前<italic>m阶</italic>导数的一族新算法。特别是，它表明，所有的衍生物可以评估在3<italic>n</italic> - 2乘法。以前的最佳结果需要1/2<italic>n</italic>（<italic>n</italic>+ 1）次乘法。一些最优性结果。
A family of new algorithms is given for evaluating the first <italic>m</italic> derivatives of a polynomial. In particular, it is shown that all derivatives may be evaluated in 3<italic>n</italic> - 2 multiplications. The best previous result required 1/2<italic>n</italic>(<italic>n</italic> + 1) multiplications. Some optimality results are presented.