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Algorithms for triangular decomposition of block Hankel and Toeplitz matrices with application to factoring positive matrix polynomials


Author: J. Rissanen
Journal: Math. Comp. 27 (1973), 147-154
MSC: Primary 65F30
DOI: https://doi.org/10.1090/S0025-5718-1973-0329235-5
MathSciNet review: 0329235
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Abstract: Algorithms are given for calculating the block triangular factors $ A,\hat A,B = {A^{ - 1}}$ and $ \hat B = {\hat A^{ - 1}}$ and the block diagonal factor D in the factorizations $ R = AD\hat A$ and $ BR\hat B = D$ of block Hankel and Toeplitz matrices R. The algorithms require $ O({p^3}{n^2})$ operations when R is an $ n \times n$-matrix of $ p \times p$-blocks.

As an application, an iterative method is described for factoring $ p \times p$-matrix valued positive polynomials $ R = \sum\nolimits_{i = - m}^m {R_i}{x^i},{R_{ - i}} = {R'_i} $, as $ \bar A(x)\bar A'({x^{ - 1}})$, where $ \bar A(x)$ is outer.


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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1973-0329235-5
Keywords: Hankel and Toeplitz matrices, triangular decomposition of matrices
Article copyright: © Copyright 1973 American Mathematical Society

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