Comparison of algorithms for computing infinite structural indices of polynomial matrices

A new algorithm is proposed to compute the infinite structural indices of a polynomial matrix, i.e. the algebraic and geometric multiplicities of its poles and zeros at infinity. The algorithm is based on numerically stable operations only, and takes full advantage of the block Toeplitz structure of a constant matrix built directly from the polynomial matrix coefficients. Comparative numerical examples and a full computational complexity analysis indicate that the Toeplitz algorithm can be viewed as a competitive alternative to the well-known state-space pencil matrix algorithm for obtaining structural indices.