The Euclidean distance degree of an algebraic variety

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

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Abstract

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.
Original languageEnglish
Publishers.n.
Number of pages42
Publication statusPublished - 2013

Publication series

NamearXiv.org
Volume1309.0049 [math.AG]

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