Complexity of Bezout's theorem V: polynomial time
Selected papers of the workshop on Continuous algorithms and complexity
Complexity of Bezout's theorem IV: probability of success; extensions
SIAM Journal on Numerical Analysis
Complexity and real computation
Complexity and real computation
On simple zeros of analytic functions of n variables
Mathematics of Computation
Kronecker's and Newton's approaches to solving: a first comparison
Journal of Complexity
How Lower and Upper Complexity Bounds Meet in Elimination Theory
AAECC-11 Proceedings of the 11th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
When Polynomial Equation Systems Can Be "Solved" Fast?
AAECC-11 Proceedings of the 11th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
On Location and Approximation of Clusters of Zeros of Analytic Functions
Foundations of Computational Mathematics
On Location and Approximation of Clusters of Zeros: Case of Embedding Dimension One
Foundations of Computational Mathematics
Estimates on the Distribution of the Condition Number of Singular Matrices
Foundations of Computational Mathematics
| Hi-index | 0.00 |
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.