一个反对称矩阵乘法的快速算法  

A Fast Algorithm of Anti-symmetric Matrix Multiplication

作　　者：王珂[1] 许波[2] 

机构地区：[1]苏州职工科技大学基础课部,江苏苏州215004 [2]江苏石油化工学院信息科学系,江苏常州213016

出　　处：《江苏石油化工学院学报》2001年第2期52-53,共2页Journal of Jiangsu Institute of Petrochemical Technology

摘　　要：矩阵乘法是数值计算中的常见问题 ,其运算阶的降低一直是人们关注的基本问题 ,而多项式求值、多项式插值及多项式求导问题迄今已出现了许多有效且稳定的快速算法。讨论了一个n阶反对称矩阵与n维列向量的乘法问题 ,证明了该问题与多项式求值问题的等价性 ,提出了一个运算阶为O (n (log2 n) 2 )的快速算法 ,并讨论了一个反对称矩阵乘法的例子 ,其O(n2 )的运算阶在反对称矩阵乘法情形至少可降低到O (n (log2 n) 2 )。The matrix multiplication is a common question in numerical caculation. For its massive caculation ,lower order of caculation is a basic question.But finding an interpolation polynomial and polynomial evaluation have been discussed extensively,many stable fast algorithms have so far been presented.In this paper ,we study a multiplication of n-order anti-symmetric matrix with vector ,and prove the equivalence of the problem with polynomial evaluation ,and describe a fast algorithm with O(n( log 2n) 2) arithmetic time complexity. Furthermore,we present an anti-symmetric matrix and illustrate that for the best algorithm of matrix multiplication,its caculation order can be dropped at least to O(n( log 2n) 2) .

关 键 词：多项式求值 快速算法 矩阵乘法 阶 反对称矩阵乘法 

分 类 号：O241.6[理学—计算数学]