Can I read There are Significantly More Nonnegative Polynomials than Sums of Squares on EtoBox?

There are Significantly More Nonnegative Polynomials than Sums of Squares by Blekherman, Grigoriy is a scholarly article available to read on EtoBox.

What is There are Significantly More Nonnegative Polynomials than Sums of Squares about?

We investigate the quantitative relationship between nonnegative polynomials and sums of squares of polynomials. We show that if the degree is fixed and the number of variables grows then there are significantly more nonnegative polynomials than sums of squares. More specifically, we take compact bases of the cone of nonnegative polynomials and the cone of sums of squares and derive bounds for the volumes of the bases. If the degree is greater than 2 then we show that the ratio of the volumes of the bases, raised to the power reciprocal to the ambient dimension, tends to 0 as the number of variables tends to infinity.

Author

Blekherman, Grigoriy

Published

2003

Language

EN