The Euclidean distance degree of an algebraic variety

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. 99-149. Springer 10.1007/s10208-014-9240-x

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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 Eckart-Young 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:

1615-3375

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/s10208-014-9240-x

ArXiv ID:

1309.0049v3

BORIS DOI:

10.7892/boris.99761

URI:

https://boris.unibe.ch/id/eprint/99761

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