The Euclidean distance degree of an algebraic variety

J. Draisma, E. Horobet, G. Ottaviani, B. Sturmfels, R.R. Thomas

Onderzoeksoutput: Bijdrage aan tijdschriftTijdschriftartikelAcademicpeer review

53 Citaten (Scopus)
3 Downloads (Pure)


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 general point outside the variety. Focusing on varieties seen in applications, we present numerous tools for exact computations.
Originele taal-2Engels
Pagina's (van-tot)99-149
TijdschriftFoundations of Computational Mathematics
Nummer van het tijdschrift1
StatusGepubliceerd - feb 2016

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