Algorithms for triangular decomposition of block Hankel and Toeplitz matrices with application to factoring positive matrix polynomials
Algorithms for triangular decomposition of block Hankel and Toeplitz matrices with application to factoring positive matrix polynomials
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块 Hankel 和 Toeplitz 矩阵的三角分解算法及其应用于因式分解正矩阵多项式
DOI：
10.1090/s0025-5718-1973-0329235-5
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发表时间：
1973
影响因子：
2
通讯作者：
J. Rissanen
中科院分区：
文献类型：
--
作者：
J. Rissanen
本文给出了块Hankel矩阵R和Toeplitz矩阵R的分解R = ADA和BR B = D中的块三角因子A，A，B = A-1和A = -'及块对角因子D的计算算法。当R是p × p-块的n × n-矩阵时，该算法需要O（p3 n2）的运算.作为应用，给出了分解p × p-矩阵值正多项式R = E7=-mRix '，R = R'，阿萨（x）A '（x-1）的迭代方法，其中A（x）是外多项式.
Algorithms are given for calculating the block triangular factors A, A, B = A-1 and A = -' and the block diagonal factor D in the factorizations R = ADA and BRB = D of block Hankel and Toeplitz matrices R. The algorithms require O(p3n2) operations when R is an n X n-matrix of p X p-blocks. As an application, an iterative method is described for factoring p X p-matrix valued positive polynomials R = E7=-m Rix', R_ = R', asA(x)A'(x-1), where A(x) is outer.