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A lifted square formulation for certifiable Schubert calculus

2015/04/04 by Hein, Nickolas, Sottile, Frank
#14N15 #14Q20 #Algebraic Geometry (math.AG) #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1504.00979

Abstract

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.

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