Numerical Schubert Calculus via the Littlewood-Richardson Homotopy Algorithm
Algebraic Geometry
2020-07-06 v3 Numerical Analysis
Numerical Analysis
Abstract
We develop the Littlewood-Richardson homotopy algorithm, which uses numerical continuation to compute solutions to Schubert problems on Grassmannians and is based on the geometric Littlewood-Richardson rule. One key ingredient of this algorithm is our new optimal formulation of Schubert problems in local Stiefel coordinates as systems of equations. Our implementation can solve problem instances with tens of thousands of solutions.
Cite
@article{arxiv.1802.00984,
title = {Numerical Schubert Calculus via the Littlewood-Richardson Homotopy Algorithm},
author = {Anton Leykin and Abraham Martin del Campo and Frank Sottile and Ravi Vakil and Jan Verschelde},
journal= {arXiv preprint arXiv:1802.00984},
year = {2020}
}
Comments
27 pages, many figures