The Inverses of Block Toeplitz Matrices | Zendy

Xiao-Guang Lv | Zendy; TingZhu Huang | Zendy

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The Inverses of Block Toeplitz Matrices

Author(s) -

Xiao-Guang Lv,

TingZhu Huang

Publication year - 2013

Publication title -

journal of mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.252

H-Index - 13

eISSN - 2314-4785

pISSN - 2314-4629

DOI - 10.1155/2013/207176

Subject(s) - toeplitz matrix , mathematics , invertible matrix , circulant matrix , block (permutation group theory) , levinson recursion , block matrix , inverse , scalar (mathematics) , matrix (chemical analysis) , combinatorics , pure mathematics , algebra over a field , eigenvalues and eigenvectors , geometry , physics , materials science , quantum mechanics , composite material

We study the inverses of block Toeplitz matrices based on the analysis of the block cyclic displacement. New formulas for the inverses of block Toeplitz matrices are proposed. We show that the inverses of block Toeplitz matrices can be decomposed as a sum of products of block circulant matrices. In the scalar case, the inverse formulas are proved to be numerically forward stable, if the Toeplitz matrix is nonsingular and well conditioned.

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