What is numerical algebraic geometry?. (March 2017)

• Record Type: Journal Article
• Authors: Hauenstein, Jonathan D.; Sommese, Andrew J.
• Is Part Of: Journal of symbolic computation. Volume 79:Part 3(2017)
• Page Start: 499
• Page End: 507
• Publication Date: 2017-03
• Subjects: 65H10 -- 68W30 -- 14Q99; Witness set -- Generic point -- Homotopy continuation -- Cascade homotopy -- Irreducible component -- Multiplicity -- Numerical algebraic geometry -- Polynomial system -- Numerical irreducible decomposition -- Primary decomposition -- Algebraic set -- Algebraic variety -- Number field; 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.2016.07.015
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: The foundation of algebraic geometry is the solving of systems of polynomial equations. When the equations to be considered are defined over a subfield of the complex numbers, numerical methods can be used to perform algebraic geometric computations forming the area of numerical algebraic geometry. This article provides a short introduction to numerical algebraic geometry with the subsequent articles in this special issue considering three current research topics: solving structured systems, certifying the results of numerical computations, and performing algebraic computations numerically via Macaulay dual spaces.