Computation of least order solutions of linear rational equations

Kurzfassung

We propose a numerically reliable approach for computing solutions of least McMillan order of linear equations with rational matrix coefficients. The main computational ingredients are the orthogonal reduction of the associated system matrix pencil to a certain Kronecker-like staircase form and the solution of a minimal dynamic cover design problem. For these computations we discuss numerically reliable algorithms relying on matrix pencil and descriptor system techniques.