Solving Schubert Problems with Littlewood-Richardson Homotopies. (arXiv:1001.4125v1 [math.NA])

We present a new numerical homotopy continuation algorithm for finding all
solutions to Schubert problems on Grassmannians. This Littlewood-Richardson
homotopy is based on Vakil's geometric proof of the Littlewood-Richardson rule.
Its start solutions are given by linear equations and they are tracked through
a sequence of homotopies encoded by certain checker configurations to find the
solutions to a given Schubert problem. For generic Schubert problems the number
of paths tracked is optimal. The Littlewood-Richardson homotopy algorithm is
implemented using the path trackers of the software package PHCpack.

Published by

Original source : http://arxiv.org/abs/1001.4125...