Ah. Sayed et T. Kailath, FAST ALGORITHMS FOR GENERALIZED DISPLACEMENT STRUCTURES AND LOSSLESS SYSTEMS, Linear algebra and its applications, 219, 1995, pp. 49-78
We derive an efficient recursive procedure for the triangular factoriz
ation of strongly regular matrices with generalized displacement struc
ture that includes, as special cases, a variety of previously studied
classes such as Toeplitz-like and Hankel-like matrices, The derivation
is based on combining a simple Gaussian elimination procedure with di
splacement structure, and leads to a transmission-like interpretation
in terms of two cascades of first-order sections. We further derive st
ate-space realizations for each section and for the entire cascades, a
nd show that these realizations satisfy a generalized embedding result
and a generalized notion of J-losslessness. The cascades turn out to
have intrinsic blocking properties, which can be shown to be equivalen
t to interpolation constrains.