Title | On the probability distribution of singular varieties of given corank |
Author(s) | Carlos , Luis Miguel Pardo |
Type | Article in Journal |
Abstract | We exhibit sharp upper bounds for the probability distribution of the distance from a system of multivariate polynomial equations to the strata of all systems having a critical zero of given corank. We also prove sharp upper bounds for the probability distribution of the condition number of singular systems of multivariate polynomial equations. We finally state a new and sharp technique of the Geometry of Numbers. Using this technique we show that rational systems of multivariate polynomial equations are equidistributed with respect to singular systems having a critical zero of given corank. |
Keywords | Polynomial equation solving, Condition number, Discrepancy bounds |
ISSN | 0747-7171 |
URL |
http://www.sciencedirect.com/science/article/pii/S0747717106000629 |
Language | English |
Journal | Journal of Symbolic Computation |
Volume | 42 |
Number | 1–2 |
Pages | 4 - 29 |
Year | 2007 |
Note | Effective Methods in Algebraic Geometry (MEGA 2005) |
Edition | 0 |
Translation |
No |
Refereed |
No |