A Primal-Dual Formulation for Certifiable Computations in Schubert Calculus
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2015, SFoCM. Formulating a Schubert problem as solutions to a system of equations in either Plcker space or local coordinates of a Schubert cell typically involves more equations than variables. We present a novel primal-dual formulation of any Schubert problem on a Grassmannian or flag manifold as a system of bilinear equations with the same number of equations as variables. This formulation enables numerical computations in the Schubert calculus to be certified using algorithms based on Smales -theory.