摘要
r-循环矩阵是实际中经常碰到的一种矩阵,其定义如下: 定义。设r为任意复数,n阶r-循环矩阵是指Toeplitz矩阵T_r=(t_(j-i))_(n×n),且满足t_(i-i)=rt_(j-i+n),当j-i<0时。
This paper considers r-circulant matrix linear systems. By using a FFT algorithm wepresent a fast algorithm for determining whether such a system is solvable or not and fin-ding its solutions if it is solvable. The cost of the algorithm is only O (nlogn) operations.If n processors are available, O (log n) steps are sufficient. When r-is zero, r-circulantmatrices become upper triangular Toeplitz matrices. We also present a parallel algorithmfor inverting such matrices, which differ from the method of [1] in the interpolation techni-que. The complexity is O(log n) steps with n^2 processors. Finally, a kind of linear cong-ruence system is considered. A method is given to turn such a system into n linear congru-ences with only one variable for each at the cost of O(n logn) operations.
出处
《数值计算与计算机应用》
CSCD
北大核心
1989年第1期36-42,共7页
Journal on Numerical Methods and Computer Applications
基金
国防科技大学基础科研基金
