摘要
循环矩阵的求逆及相乘的算法,无论在理论上还是在实际应用中都具有非常重要的意义.本文不从计算Jordan标准形式或特征值出发,而是利用矩阵乘法及逆矩阵的一些简单性质,给出了n阶(n1,n2)型二重(r1,r2) 循环矩阵求逆、两个n阶(n1,n2)型二重(r1,r2) 循环矩阵相乘的直接计算方法,推广了已有的结果.这些算法已编到C++源代码在服务器上通过,验证了这些算法是稳定的有效的.若用快速富里叶变换(FFT)计算,这些算法的时间复杂性均为O(n1n2log2n1n2).
The algorithms for evaluating inverse matrices and multiplication of circulant matrices, are very important on the theoreties as well as application. In this paper, the direct methods for evaluating inverse matrices and multiplication of level-2.(r_1,r_2)-circulant matrix of type(n_1,n_2) of order n are presented. This algorithms only use some simple multiplications of matrices or basic properties of inverse matrix, and it needn't start from caculating the Jordan's normal form or eigenvalues of matrices ,generalized the already results. This algorithms has been programed to C++ source code and passed, proved that this algorithms are stable aand effective. If we use FFT , their computation time complexity are all O(n_1n_2 log_2 n_1n_2).
出处
《科技通报》
北大核心
2004年第2期89-94,共6页
Bulletin of Science and Technology
基金
国家自然科学基金资助项目(9971024)
浙江省自然科学基金资助项目(199047)
关键词
计算数学
n阶(n1
n2)型二重(r1
r2)-循环矩阵
逆矩阵
矩阵相乘
算法复杂性
computatinal mathematics
Level-2.(r_1,r_2)-Circulant Matrix of Type(n_1,n_2) of order n
inverse matrix
multiplication of matrices
algorithm and time complexity
