Numerical Schubert Calculus via the LittlewoodRichardson Homotopy Algorithm
Abstract
We develop the LittlewoodRichardson homotopy algorithm, which uses numerical continuation to compute solutions to Schubert problems on Grassmannians and is based on the geometric LittlewoodRichardson 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.
 Publication:

arXiv eprints
 Pub Date:
 February 2018
 arXiv:
 arXiv:1802.00984
 Bibcode:
 2018arXiv180200984L
 Keywords:

 Mathematics  Algebraic Geometry;
 Mathematics  Numerical Analysis;
 14N15;
 65H10
 EPrint:
 27 pages, many figures