Fast algorithms for generalized displacement structures and lossless systems

We derive an efficient recursive procedure for the triangular factorization of strongly regular matrices with generalized displacement structure 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 displacement structure, and leads to a transmission-like interpretation in terms of two cascades of first-order sections. We further derive state-space realizations for each section and for the entire cascades, and 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 equivalent to interpolation constrains.