2014/06/03 by Hauenstein, Jonathan D., Hein, Nickolas, Sottile, Frank
#14N15 #14Q20 #Algebraic Geometry (math.AG) #FOS: Mathematics #Numerical Analysis (math.NA)
paper · doi:10.48550/arxiv.1406.0864
Formulating a Schubert problem as the solutions to a system of equations in either Plücker space or in the 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 Smale's α-theory.