PIERI HOMOTOPIES FOR PROBLEMS IN ENUMERATIVE GEOMETRY APPLIED TO POLE PLACEMENT IN LINEAR

SYSTEMS CONTROL

BIRKETT HUBER JAN VERSCHELDE

Abstract. In the numerical Schubert calculus paper, Pieri homotopies were proposed turning the deformation arguments of classical Schubert calculus into effective numerical methods by expressing the deformations algebraically and applying numerical path following techniques. In this paper we describe the Pieri homotopy algorithm in terms of a poset of simpler problems. This approach is more intuitive and more suitable for computer implementation than the original description. It also provides a self-contained proof of correctness. We were able to extend our approach to the quantum Schubert calculus. Our approach mirrors existing counting methods for this problem and yields a numerical implementation for the dynamic pole placement problem.