【摘要】 <正> 1.引言 线性系统理论中,一个系统的可观测性与可控性及数据拟合中若干问题均化为Toeplitz矩阵的研究。近年来,有关Toeplitz矩阵,Toeplitz三角阵,块Toeplitz矩阵及块Toeplitz三角阵的性质及相应算法的研究有了很大的进展([1]、[2]、[3]、[4])。早在1964,1965年,W.F.Trench[5]、[6]给出n阶Toeplitz矩阵求逆算法,计算复杂性为O(n~2),S.Zohar更多还原

【Abstract】 In this paper, it is showed that the computational complexity of inversion of block triangular Toeplitz matrix U= (U0, U1,…, Un-1 ) is O (m2nlogn + m3), as well as solution of block triangla r Toeplitz linear systems, where U ’s are m×m mat rices. By using this results, we reduce arithmetic operations of division of polynomials from O(nlog2n) to O(nlogn).更多还原