Rank properties of a sequence of block bidiagonal Toeplitz matrices
Grigoris I. Kalogeropoulos, Athanasios D. Karageorgos, Marilena Mitrouli, Athanasios A. Pantelous · Neural, Parallel & Scientific Computations archive · 2010
In the present paper, we proposed a new efficient rank updating methodology for evaluating the rank (or equivalently the nullity) of a sequence of block diagonal Toeplitz matrices. The results are applied to a variation of the partial realization problem. Characteristically, this sequence of block matrices is a basis for the computation of the Weierstrass canonical form of a matrix pencil that appeared in many practical numerical applications in control theory.