Gohberg-Semencul type formulas via embedding of Lyapunov equations (signal processing)
D. Pal · IEEE Transactions on Signal Processing · 1993
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 Sigma -lossless embedding of Lyapunov equations. It has been shown that if a nonsingular matrix R has Toeplitz displacement inertia (p, q), then R/sup -1/ does not have the same Toeplitz displacement inertia. However, a para-Hermitian conjugate of R/sup -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 embedding.>