Integration and Optimization of Multivariate Polynomials by Restriction onto a Random Subspace
dc.contributor.author | Barvinok, Alexander I. | en_US |
dc.date.accessioned | 2006-09-11T16:32:51Z | |
dc.date.available | 2006-09-11T16:32:51Z | |
dc.date.issued | 2006-03-06 | en_US |
dc.identifier.citation | Barvinok, Alexander; (2006). "Integration and Optimization of Multivariate Polynomials by Restriction onto a Random Subspace." Foundations of Computational Mathematics (): -. <http://hdl.handle.net/2027.42/45853> | en_US |
dc.identifier.issn | 1615-3375 | en_US |
dc.identifier.issn | 1615-3383 | en_US |
dc.identifier.uri | https://hdl.handle.net/2027.42/45853 | |
dc.description.abstract | 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. | en_US |
dc.format.extent | 257913 bytes | |
dc.format.extent | 3115 bytes | |
dc.format.mimetype | application/pdf | |
dc.format.mimetype | text/plain | |
dc.language.iso | en_US | |
dc.publisher | Springer-Verlag; Springer | en_US |
dc.subject.other | Applications of Mathematics | en_US |
dc.subject.other | Mathematics | en_US |
dc.subject.other | Wick Formula | en_US |
dc.subject.other | Random Subspaces | en_US |
dc.subject.other | Polynomials | en_US |
dc.subject.other | Computer Science, General | en_US |
dc.subject.other | Math Applications in Computer Science | en_US |
dc.subject.other | Linear and Multilinear Algebras, Matrix Theory | en_US |
dc.subject.other | Numerical Analysis | en_US |
dc.subject.other | Integration | en_US |
dc.subject.other | Algorithms | en_US |
dc.subject.other | Gaussian Measure | en_US |
dc.title | Integration and Optimization of Multivariate Polynomials by Restriction onto a Random Subspace | en_US |
dc.type | Article | en_US |
dc.subject.hlbsecondlevel | Philosophy | en_US |
dc.subject.hlbsecondlevel | Computer Science | en_US |
dc.subject.hlbtoplevel | Humanities | en_US |
dc.subject.hlbtoplevel | Engineering | en_US |
dc.description.peerreviewed | Peer Reviewed | en_US |
dc.contributor.affiliationum | Department of Mathematics, University of Michigan, Ann Arbor, MI 48109-1043, USA | en_US |
dc.contributor.affiliationumcampus | Ann Arbor | en_US |
dc.description.bitstreamurl | http://deepblue.lib.umich.edu/bitstream/2027.42/45853/1/10208_2005_Article_178.pdf | en_US |
dc.identifier.doi | http://dx.doi.org/10.1007/s10208-005-0178-x | en_US |
dc.identifier.source | Foundations of Computational Mathematics | en_US |
dc.owningcollname | Interdisciplinary and Peer-Reviewed |
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