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arXiv · 1309.0049

The Euclidean distance degree of an algebraic variety

Jan Draisma·Emil Horobet·Giorgio Ottaviani·Bernd Sturmfels·Rekha 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.

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Jan Draisma, Emil Horobet, Giorgio Ottaviani, Bernd Sturmfels, Rekha R. Thomas. 2014-11-27. The Euclidean distance degree of an algebraic variety. https://arxiv.org/abs/1309.0049

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