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Numerical Schubert calculus via the Littlewood-Richardson homotopy algorithm
Mathematics of Computation ( IF 2 ) Pub Date : 2021-02-04 , DOI: 10.1090/mcom/3579
Anton Leykin , Abraham Martín del Campo , Frank Sottile , Ravi Vakil , Jan Verschelde

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.

中文翻译:

基于 Littlewood-Richardson 同伦算法的数值舒伯特演算

我们开发了 Littlewood-Richardson 同伦算法,该算法使用数值延拓来计算 Grassmannians 上 Schubert 问题的解,并基于几何 Littlewood-Richardson 规则。该算法的一个关键要素是我们在局部 Stiefel 坐标系中将舒伯特问题的新优化公式化为方程组。我们的实现可以用数以万计的解决方案来解决问题实例。
更新日期:2021-02-04
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