English

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.

Keywords

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

R2 v1 2026-06-22T04:29:54.089Z