A Primal-Dual Formulation for Certifiable Computations in Schubert Calculus

abstract

• 2015, SFoCM. Formulating a Schubert problem as solutions to a system of equations in either Plcker space or 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 Smales -theory.

authors

• Sottile, Frank

published proceedings

• Foundations of Computational Mathematics

author list (cited authors)

• Hauenstein, J. D., Hein, N., & Sottile, F.

citation count

• 4

complete list of authors

• Hauenstein, Jonathan D||Hein, Nickolas||Sottile, Frank

publication date

• August 2016

publisher

• Springer Nature  Publisher

published in

• Foundations of Computational Mathematics  Journal

keywords

• 49 Mathematical Sciences
• 4903 Numerical And Computational Mathematics
• 4904 Pure Mathematics

Digital Object Identifier (DOI)

• 10.1007/s10208-015-9270-z

start page

• 941

end page

• 963

volume

• 16

issue

• 4

URL

• http://dx.doi.org/10.1007/s10208-015-9270-z