Computing minimal partial realizations via a Lanczos-type algorithm for multiple starting vectors
R.W. Freund · 2002
We describe a Lanczos-type procedure that reduces a given realization of a finite sequence of (moment) matrices to a minimal partial realization. A key feature of this procedure is that the underlying Lanczos-type algorithm is directly applied to the matrix triplet describing the given realization, rather than to the moment matrices. It thus avoids explicit formulation of and the usually unstable computation with the moment matrices.