High Probability Analysis of the Condition Number of Sparse Polynomial Systems

Details High Probability Analysis of the Condition Number of Sparse Polynomial Systems High Probability Analysis of the Condition Number of Sparse Polynomial Systems

2002-12-12

arxiv.org/abs/math/0212179v1

Theoretical Computer Science, Volume 315, Issues 2-3, 6 May 2004, Pages 525-555.

Mathematics

Numerical Analysis

29 pages, no figures. Extensive revision and streamlining of math.NA/0012104. In particular, new theorem with explicit high pr

Scientific paper

10.1016/j.tcs.2004.01.006

Let F:=(f_1,...,f_n) be a random polynomial system with fixed n-tuple of supports. Our main result is an upper bound on the probability that the condition number of f in a region U is larger than 1/epsilon. The bound depends on an integral of a differential form on a toric manifold and admits a simple explicit upper bound when the Newton polytopes (and underlying covariances) are all identical. We also consider polynomials with real coefficients and give bounds for the expected number of real roots and (restricted) condition number. Using a Kahler geometric framework throughout, we also express the expected number of roots of f inside a region U as the integral over U of a certain {\bf mixed volume} form, thus recovering the classical mixed volume when U = (C^*)^n.

Affiliated with

Also associated with

No associations

Rating

High Probability Analysis of the Condition Number of Sparse Polynomial Systems 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 High Probability Analysis of the Condition Number of Sparse Polynomial Systems, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and High Probability Analysis of the Condition Number of Sparse Polynomial Systems will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-344771