摘要
指出了文《R-循环分块矩阵求逆的快速傅里叶算法》[1]中的一个错误,并证明了n阶r-循环矩阵的m次方根矩阵中仍为r-循环矩阵的矩阵个数为mn,进一步给出了求n阶r-循环矩阵的m次方根矩阵中仍为r-循环矩阵的矩阵的快速算法,若用FFT计算一个m次方根矩阵,其时间复杂性为O(nlog2n);计算全部平方根矩阵的时间复杂性为O(nmn)。同时,本文还给出了求r-循环矩阵主平方根矩阵的算法。
In this paper, a mistake in ＂The fast fourier algorithm for the inverse of R-Block circulant matrices＂ is pointed out. It can prove that the quantity of all mth root of r-cireulant matrix which are still r-cireulant matrices is m^n, and a fast algorithm for calculating all mth root of r-circulant matrix which are still r-eirculant matrices is gived. It can prove that the computation time complexity is O（nlog2n） for calculating one mth root of r-cireulant matrix and which is O（nm^n） for calculating all by using FFT. At the same time, an algorithm for computing the principal square root of matrix is gived.
出处
《科技通报》
2007年第1期6-10,共5页
Bulletin of Science and Technology
基金
浙江省教育厅科研计划项目(20061554)
