# The Euclidean Distance Degree of an Algebraic Variety

@article{Draisma2016TheED, title={The Euclidean Distance Degree of an Algebraic Variety}, author={Jan Draisma and Emil Horobet and Giorgio Ottaviani and Bernd Sturmfels and Rekha R. Thomas}, journal={Foundations of Computational Mathematics}, year={2016}, volume={16}, pages={99-149} }

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…

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