The Inverses of Block Hankel and Block Toeplitz Matrices
نویسندگان
چکیده
منابع مشابه
The Inverses of Block Hankel and Block Toeplitz Matrices
A set of new formulae for the inverse of a block Hankel (or block Toeplitz) matrix is given. The formulae are expressed in terms of certain matrix Pad6 forms, which approximate a matrix power series associated with the block Hankel matrix. By using Frobenius-type identities between certain matrix Pad6 forms, the inversion formulae are shown to generalize the formulae of Gohberg-Heinig and, in t...
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We consider the inversion of block tridiagonal, block Toeplitz matrices and comment on the behaviour of these inverses as one moves away from the diagonal. Using matrix Möbius transformations, we first present an O(1) representation (with respect to the number of block rows and block columns) for the inverse matrix and subsequently use this representation to characterize the inverse matrix. The...
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In this paper, we consider the approximation of dense block Toeplitz-plus-Hankel matrices by sums of Kronecker products. We present an algorithm for efficiently computing the matrix approximation that requires the factorization of matrices of much smaller dimension than that of the original. The main results are described for block Toeplitz matrices with Toeplitz-plus-Hankel blocks (BTTHB), but...
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A structured total least squares problem is considered in which the extended data matrix is partitioned into blocks and each of the blocks is block-Toeplitz/Hankel structured, unstructured, or exact. An equivalent optimization problem is derived and its properties are established. The special structure of the equivalent problem enables us to improve the computational efficiency of the numerical...
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The inversion problem for square matrices having the structure of a block Hankel-like matrix is studied. Examples of such matrices in&de Hankel striped, Hankel layered, and vector Hankel matrices. It is shown that the components that both determine nonsingularity and construct the inverse of such matrices are closely related to certain matrix polynomials. These matrix polynomials are multidimen...
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ژورنال
عنوان ژورنال: SIAM Journal on Computing
سال: 1990
ISSN: 0097-5397,1095-7111
DOI: 10.1137/0219006