块r—循环阵和块对称r—循环阵及有关算法的计算复杂性

The Block r-CircuIant Matrix and the Block Symmetric r-Circulant Matrix and the Computation Time Complexity of Some Related Algorithems

本文给出了nm阶块r-循环阵BC_r(A_0,A_1,…,A_(n-1)和nm阶块对称r-循环阵BSC_r(A_0,A_1,…,A_(n-1))的一些性质,其中A_p(p=0,n-1)为m阶方阵,并利用FFT(快速富里叶变换)证明了有关算法的计算复杂性为O(m^2nlog_2n+nm^3)。

In this paper, we gave some properties of block r-circulant matrix BC(A0,A1,…,An-1) and block symmetric r-circulant matrix BSCr(A0,A1,…,An-1), where A (p =0,n-1) are the matrix of n order, and proved that the computation time complexity of some related algorithms is O(m 2nlog2n) + nm3).