一类范德蒙行列式几种算法的分析与比较

黄伟亮 刘辉

摘要：分别采用按行列展开法、范德蒙公式法及进一步的简化算法对一类特殊的范德蒙行列式进行求值。首先分析了前两种算法的基本思想方法，并给出了另一个较为简洁的计算方法，其次，给出了三种算法的编码实现。理论分析和实验结果表明，进一步的简化算法在计算该类范德蒙行列式时，效果最佳。

关键词： 范德蒙行列式；n次本原单位根；算法

中图分类号：TP301 文献标识码：A 文章编号：1009-3044（2015）05-0078-02

Comparison and Analysis of Several Algorithm for a Class of Vandermonde Determinant

HUANG Wei-liang， LIU Hui

（Department of Information Engineering， Henan Mechanical and Electrical Vocational College， Zhenzhou 451191， China）

Abstract： The row or column expansion method， Vandermonde formula method， and a simplified algorithm are applied to calculate the value of a special class of Vandermonde determinant respectively. Firstly， the paper analyzes the basic idea of the previous two methods， and gives another simple calculation method. Secondly， the ways to realize their encoding are listed. Both the theoretical analyses and experimental results indicate that the simplified algorithm listed here is the most effective method to calculate the value of this class of Vandermonde determinant.

Key words： Vandermonde determinant； nth primitive root of unity； algorithm；