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 general point outside the variety. Focusing on varieties seen in applications, we present numerous tools for exact computations. |
Year | DOI | Venue |
|---|---|---|
2016 | https://doi.org/10.1007/s10208-014-9240-x | Foundations of Computational Mathematics |
Keywords | Field | DocType |
Distance minimization,Computational algebraic geometry,Duality,Polar classes,Low-rank approximation,51N35,14N10,14M12,90C26,13P25,15A69 | Singular point of an algebraic variety,Dimension of an algebraic variety,Mathematical optimization,Function field of an algebraic variety,Mathematical analysis,Euclidean distance,Algebraic surface,Algebraic cycle,Real algebraic geometry,Euclidean distance matrix,Mathematics | Journal |
Volume | Issue | Citations |
16 | 1 | 35 |
PageRank | References | Authors |
2.26 | 8 | 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 |