Integration and Optimization of Multivariate Polynomials by Restriction onto a Random Subspace

Details Integration and Optimization of Multivariate Polynomials by Restriction onto a Random Subspace Integration and Optimization of Multivariate Polynomials by Restriction onto a Random Subspace

2005-02-14

arxiv.org/abs/math/0502298v1

Mathematics

Optimization and Control

15 pages

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Integration and Optimization of Multivariate Polynomials by Restriction onto a Random Subspace does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Integration and Optimization of Multivariate Polynomials by Restriction onto a Random Subspace, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Integration and Optimization of Multivariate Polynomials by Restriction onto a Random Subspace will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-242787