Integration and Optimization of Multivariate Polynomials by Restriction onto a Random Subspace
| dc.creator | Barvinok, Alexander | |
| dc.date | 2005-02-14 | |
| dc.date.accessioned | 2026-07-07T05:17:00Z | |
| dc.date.available | 2026-07-07T05:17:00Z | |
| dc.description | We consider the problem of efficient integration of an n-variate polynomial with respect to the Gaussian measure in R^n and related problems of complex integration and optimization of a polynomial on the unit sphere. We identify a class of n-variate polynomials f for which the integral of any positive integer power f^p over the whole space is well-approximated by a properly scaled integral over a random subspace of dimension O(log n). Consequently, the maximum of f on the unit sphere is well-approximated by a properly scaled maximum on the unit sphere in a random subspace of dimension O(log n). We discuss connections with problems of combinatorial counting and applications to efficient approximation of a hafnian of a positive matrix. | |
| dc.description | 15 pages | |
| dc.identifier | https://arxiv.org/abs/math/0502298 | |
| dc.identifier | http://arxiv.org/abs/math/0502298 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/74199 | |
| dc.subject | Optimization and Control | |
| dc.subject | Combinatorics | |
| dc.subject | 68W20, 68W25, 60D05, 90C26 | |
| dc.title | Integration and Optimization of Multivariate Polynomials by Restriction onto a Random Subspace | |
| dc.type | text |