Numerical Schubert calculus via the Littlewood-Richardson homotopy algorithm

Leykin, Anton; Martín del Campo, Abraham; Sottile, Frank; Vakil, Ravi; Verschelde, Jan

doi:10.1090/mcom/3579

Numerical Schubert calculus via the Littlewood-Richardson homotopy algorithm
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by Anton Leykin, Abraham Martín del Campo, Frank Sottile, Ravi Vakil and Jan Verschelde HTML | PDF

Math. Comp. 90 (2021), 1407-1433

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.

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