A primal-dual formulation for certifiable computations in Schubert calculus
Algebraic Geometry
2015-03-23 v2 Numerical Analysis
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.
Cite
@article{arxiv.1406.0864,
title = {A primal-dual formulation for certifiable computations in Schubert calculus},
author = {Jonathan D. Hauenstein and Nickolas Hein and Frank Sottile},
journal= {arXiv preprint arXiv:1406.0864},
year = {2015}
}
Comments
21 pages