Generalized inversion of block Toeplitz matrices
Generalized inversion of block Toeplitz matrices
复制标题
DOI：
10.1016/s0024-3795(97)00304-2
复制
发表时间：
1998-04-15
影响因子：
1.1
通讯作者：
Adukov, VM
中科院分区：
文献类型：
--
作者：
Adukov, VM
对有限块Toeplitz矩阵提出了一种类似的Wiener-Hopf分解方法。对于任意有理矩阵多项式，引入了本质指标和多项式的概念。这些概念之间的连接和Wiener-Hopf分解的一些块三角矩阵函数进行了研究。利用块Toeplitz矩阵符号的指数和本质多项式，给出了块Toeplitz矩阵的广义（单侧、双侧）逆的计算公式。作为该公式的特例，得到了一些著名的反演公式。(C)1998年爱思唯尔科学公司
An analog of a Wiener-Hopf factorization method is proposed for finite block Toeplitz matrices. For an arbitrary rational matrix polynomial, notions of essential indices and polynomials are introduced. A connection between these notions and a Wiener-Hopf factorization of some block triangular matrix functions is studied. A formula for a generalized (one-sided, two-sided) inversion of a block Toeplitz matrix is found in terms of indices and essential polynomials of its symbol. Well-known inversion formulas are obtained as special cases of this formula. (C) 1998 Elsevier Science Inc.