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 language | English |
---|

Publisher | s.n. |
---|

Number of pages | 42 |
---|

Publication status | Published - 2013 |
---|

Name | arXiv.org |
---|

Volume | 1309.0049 [math.AG] |
---|