Abstract of December 8th
IMO Seminar by Dennis Michaels
Nonnegative Polynomials
This talk deals with:
- Hilbert's 17th problem
- Real closed fields
- The cone of all homogeneous positive semidefinite polynomials of fixed
degree
- The cone of all homogeneous sum of square polynomials of fixed degree
- Extremal points of these two cones
- Deciding whether a polynomial is a sum of square, and finding a sum of
square decomposition for a sum of square polynomial
References:
B. Reznick: "Sum of Square Polynomials", Talk, Summer school
Klagenfurt, September 2005.
B. Reznick: "Some concrete aspects of Hilbert's seventeenth problem",
In: Contemporary Mathematics, vol 253, pp 251--272, AMS 2000.
Powers, Woermann: "An algorithm for sums of squares of real polynomials."
Journal of pure and applied algebra, 127, pp 99--104, (1998).