A lifted square formulation for certifiable Schubert calculus

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• 作者：Nickolas Hein^a ; ^{nhein@benedictine.edu" class="auth_mail" title="E-mail the corresponding author} ; ; Frank Sottile^b ; ^{sottile@math.tamu.edu" class="auth_mail" title="E-mail the corresponding author} ;
• 关键词：14N15 ; 14Q20
• 刊名：Journal of Symbolic Computation
• 出版年：2017
• 出版时间：March-April 2017
• 年：2017
• 卷：79
• 期：part_P3
• 页码：594-608
• 全文大小：405 K

文摘

Formulating a Schubert problem as the solutions to a system of equations in either Plücker space or in the local coordinates of a Schubert cell usually involves more equations than variables. Using reduction to the diagonal, we previously gave a primal–dual formulation for Schubert problems that involved the same number of variables as equations (a square formulation). Here, we give a different square formulation by lifting incidence conditions which typically involves fewer equations and variables. Our motivation is certification of numerical computation using Smale's α-theory.