Name
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 computation. |
Year | DOI | Venue |
|---|---|---|
2014 | 10.1145/2631948.2631951 | SNC |
Keywords | Field | DocType |
nearest point map,chern class,dual variety,euclidean distance,symbolic and numerical computation,general,optimization,polynomial optimization,computing critical points | Sum of radicals,Singular point of an algebraic variety,Discrete mathematics,Dimension of an algebraic variety,Minkowski distance,Distance from a point to a plane,Euclidean distance,Distance from a point to a line,Euclidean distance matrix,Mathematics | Conference |
Citations | PageRank | References |
3 | 0.41 | 4 |
Authors | ||
5 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Jan Draisma | 1 | 39 | 3.07 |
| Emil Horobet | 2 | 39 | 3.07 |
| Giorgio Ottaviani | 3 | 138 | 11.93 |
| Bernd Sturmfels | 4 | 926 | 136.85 |
| Rekha R. Thomas | 5 | 323 | 39.68 |