Numerical Schubert calculus
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
1997
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| _version_ | 1866912655075180544 |
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| author | Huber, Birkett Sottile, Frank Sturmfels, Bernd |
| author_facet | Huber, Birkett Sottile, Frank Sturmfels, Bernd |
| contents | We develop numerical homotopy algorithms for solving systems of polynomial equations arising from the classical Schubert calculus. These homotopies are optimal in that generically no paths diverge. For problems defined by hypersurface Schubert conditions we give two algorithms based on extrinsic deformations of the Grassmannian: one is derived from a Gröbner basis for the Plücker ideal of the Grassmannian and the other from a SAGBI basis for its projective coordinate ring. The more general case of special Schubert conditions is solved by delicate intrinsic deformations, called Pieri homotopies, which first arose in the study of enumerative geometry over the real numbers. Computational results are presented and applications to control theory are discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_alg_geom_9706004 |
| institution | arXiv |
| publishDate | 1997 |
| record_format | arxiv |
| spellingShingle | Numerical Schubert calculus Huber, Birkett Sottile, Frank Sturmfels, Bernd Algebraic Geometry Numerical Analysis Optimization and Control Primary 65H10 Secondary 14N10, 14M15 We develop numerical homotopy algorithms for solving systems of polynomial equations arising from the classical Schubert calculus. These homotopies are optimal in that generically no paths diverge. For problems defined by hypersurface Schubert conditions we give two algorithms based on extrinsic deformations of the Grassmannian: one is derived from a Gröbner basis for the Plücker ideal of the Grassmannian and the other from a SAGBI basis for its projective coordinate ring. The more general case of special Schubert conditions is solved by delicate intrinsic deformations, called Pieri homotopies, which first arose in the study of enumerative geometry over the real numbers. Computational results are presented and applications to control theory are discussed. |
| title | Numerical Schubert calculus |
| topic | Algebraic Geometry Numerical Analysis Optimization and Control Primary 65H10 Secondary 14N10, 14M15 |
| url | https://arxiv.org/abs/alg-geom/9706004 |