Draisma, Jan; Horobet, Emil; Ottaviani, Giorgio; Sturmfels, Bernd; Thomas, Rekha R. (2016). The Euclidean distance degree of an algebraic variety. Foundations of computational mathematics, 16(1), pp. 99149. Springer 10.1007/s102080149240x

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The nearest point map of a real algebraic variety with respect to Euclidean distance is an algebraic function. For instance, for varieties of low rank matrices, the EckartYoung Theorem states that this map is given by the singular value decomposition. This article develops a theory of such nearest point maps from the perspective of computational algebraic geometry. The Euclidean distance degree of a variety is the number of critical points of the squared distance to a generic point outside the variety. Focusing on varieties seen in applications, we present numerous tools for exact computations.
Item Type: 
Journal Article (Original Article) 

Division/Institute: 
08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics 
UniBE Contributor: 
Draisma, Jan 
Subjects: 
500 Science > 510 Mathematics 
ISSN: 
16153375 
Publisher: 
Springer 
Language: 
English 
Submitter: 
Olivier Bernard Mila 
Date Deposited: 
03 Aug 2017 08:57 
Last Modified: 
21 Sep 2017 08:06 
Publisher DOI: 
10.1007/s102080149240x 
ArXiv ID: 
1309.0049v3 
BORIS DOI: 
10.7892/boris.99761 
URI: 
https://boris.unibe.ch/id/eprint/99761 