Mathematics – Numerical Analysis
Scientific paper
2000-12-13
Mathematics
Numerical Analysis
48 pages, 1 figure
Scientific paper
Let f:=(f^1,\...,f^n) be a sparse random polynomial system. This means that each f^i has fixed support (list of possibly non-zero coefficients) and each coefficient has a Gaussian probability distribution of arbitrary variance. We express the expected number of roots of f inside a region U as the integral over U of a certain mixed volume form. When U = (C^*)^n, the classical mixed volume is recovered. The main result in this paper is a bound on the probability that the condition number of f on the region U is larger than 1/epsilon. This bound depends on the integral of the mixed volume form over U, and on a certain intrinsic invariant of U as a subset of a toric manifold. Polynomials with real coefficients are also considered, and bounds for the expected number of real roots and for the condition number are given. The connection between zeros of sparse random polynomial systems, Kahler geometry, and mechanics (momentum maps) is discussed.
Malajovich Gregorio
Rojas Maurice J.
No associations
LandOfFree
Random 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 Random Sparse Polynomial Systems, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Random Sparse Polynomial Systems will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-652771