The Euclidean distance degree of Fermat hypersurfaces. (May 2017)

• Record Type: Journal Article
• Authors: Lee, Hwangrae
• Is Part Of: Journal of symbolic computation. Volume 80:Part 2(2017)
• Page Start: 502
• Page End: 510
• Publication Date: 2017-05
• Subjects: Euclidean distance degree -- Fermat hypersurface -- Optimization; 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.2016.07.006
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: Finding the point in an algebraic variety that is closest to a given point is an optimization problem with many applications. We study the case when the variety is a Fermat hypersurface. Our formula for its Euclidean distance degree is a piecewise polynomial whose pieces are defined by subtle congruence conditions.