黃偉亮 劉輝

摘要：分別采用按行列展開法、范德蒙公式法及進一步的簡化算法對一類特殊的范德蒙行列式進行求值。首先分析了前兩種算法的基本思想方法，并給出了另一個較為簡潔的計算方法，其次，給出了三種算法的編碼實現(xiàn)。理論分析和實驗結(jié)果表明，進一步的簡化算法在計算該類范德蒙行列式時，效果最佳。

關(guān)鍵詞： 范德蒙行列式；n次本原單位根；算法

中圖分類號：TP301 文獻標識碼：A 文章編號：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；