Numerical Schubert Calculus via the Littlewood-Richardson Homotopy Algorithm

Anton Leykin, Abraham Martin del Campo, Frank Sottile, Ravi Vakil, and Jan Verschelde


We describe the Littlewood-Richardson homotopy algorithm, which uses numerical continuation to compute solutions of Schubert problems on Grassmannians and is based on the geometric Littlewood-Richardson rule. We provide algorithmic details and discuss its mathematical aspects. We also give an efficient formulation of Schubert problems in local Stiefel coordinates as systems of equations.