| 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 |
