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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1309.0049.pdf - Accepted Version Available under License Publisher holds Copyright. Download (1MB) | Preview |
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The Euclidean Distance Degree of an Algebraic Variety.pdf - Published Version Available under License Publisher holds Copyright. Download (1MB) | Preview |
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: |
05 Dec 2022 15:05 |
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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