Gohberg-Semencul type formulas via embedding of Lyapunov equations (signal processing)
- 1 June 1993
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Signal Processing
- Vol. 41 (6), 2208-2215
- https://doi.org/10.1109/78.218147
Abstract
The authors present a new way of deriving Gohberg-Semencul-type inversion formulas for Hermitian Toeplitz and quasi-Toeplitz matrices. The approach is based on a certain Σ-lossless embedding of Lyapunov equations. It has been shown that if a nonsingular matrix R has Toeplitz displacement inertia {p, q}, then R-1 does not have the same Toeplitz displacement inertia. However, a para-Hermitian conjugate of R-1 will have this property. It is also shown that the Gohberg-Semencul-type inversion formulas can be formed directly in terms of certain parameters of the embeddingKeywords
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