Numerical Schubert calculus via the Littlewood-Richardson homotopy algorithm

Autor:	Ravi Vakil, Abraham Martín del Campo, Anton Leykin, Jan Verschelde, Frank Sottile
Rok vydání:	2021
Předmět:	Schubert calculus MathematicsofComputing_NUMERICALANALYSIS Homotopy algorithm 010103 numerical & computational mathematics System of linear equations Mathematics::Algebraic Topology 01 natural sciences 14N15 65H10 Mathematics - Algebraic Geometry Grassmannian FOS: Mathematics Mathematics - Numerical Analysis 0101 mathematics Mathematics::Representation Theory Littlewood–Richardson rule Algebraic Geometry (math.AG) Mathematics Mathematics::Combinatorics Algebra and Number Theory Applied Mathematics 010102 general mathematics Numerical Analysis (math.NA) Algebra Computational Mathematics Numerical continuation Key (cryptography)
Zdroj:	Mathematics of Computation. 90:1407-1433
ISSN:	1088-6842 0025-5718
Popis:	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. Comment: 27 pages, many figures
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::117d8af55347cccab9b061ff1b3e994e https://doi.org/10.1090/mcom/3579 Zobrazit plný text záznamu