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A Primal-Dual Formulation for Certifiable Computations in Schubert Calculus |
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| Authors: | Jonathan D Hauenstein Nickolas Hein Frank Sottile |
| Institution: | 1.Department of Applied and Computational Mathematics and Statistics,University of Notre Dame,Notre Dame,USA;2.Department of Mathematics,University of Nebraska at Kearney,Kearney,USA;3.Department of Mathematics,Texas A&M University,College Station,USA |
| Abstract: | Formulating a Schubert problem as solutions to a system of equations in either Plücker 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 Smale’s \(\alpha \)-theory. |
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