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arXiv · 1406.0864

A primal-dual formulation for certifiable computations in Schubert calculus

Jonathan D. Hauenstein·Nickolas Hein·Frank Sottile
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Abstract

Formulating a Schubert problem as the solutions to a system of equations in either Pl\"ucker 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 \alpha-theory.

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Jonathan D. Hauenstein, Nickolas Hein, Frank Sottile. 2014-06-03. A primal-dual formulation for certifiable computations in Schubert calculus. https://arxiv.org/abs/1406.0864

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