LUCA GEMIGNANI

A numerical approach to the solution of stable resultant linear systems

dedicated to the memory of Giulio Di Cola

Pages: 259-291
Received: 17 July 2000   
Mathematics Subject Classification (2000): 65F05

Abstract: Devising efficient methods for the solution of resultant linear systems is a relevant issue in many diverse fields like computer algebra, control theory, signal processing and data modeling. Over the years, several fast and superfast algorithms have been proposed that are based either on purely numerical techniques or on mixed numeric-symbolic procedures. In this paper we present a new solution scheme falling in the former class that works under some auxiliary conditions on the separation of the spectrum of the polynomials associated with the initial coefficient matrix. Such assumptions are usually satisfied in the considered applications of control and signal theory and their exploitation allows us to reduce the original matrix problem to the equivalent one of finding the reciprocal of a Laurent polynomial. To carry out this computation we develop both finite and iterative processes employing a blend of ideas from structured numerical linear algebra, computational complex analysis and linear operator theory. The effectiveness and the robustness of the resulting composite solution methods is then confirmed by means of numerical experiments that are finally reported and discussed.