A lifted square formulation for certifiable Schubert calculus. (March 2017)

• Record Type: Journal Article
• Authors: Hein, Nickolas; Sottile, Frank
• Is Part Of: Journal of symbolic computation. Volume 79:Part 3(2017)
• Page Start: 594
• Page End: 608
• Publication Date: 2017-03
• Subjects: 14N15 -- 14Q20; Schubert calculus -- Square systems -- Certification; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2016.07.021
• Languages: English
• ISSNs: 0747-7171

Abstract

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.