An elementary recursive bound for effective Positivstellensatz and Hilbert 17-th problem
Algebraic Geometry
2017-04-12 v3
Abstract
We prove elementary recursive bounds in the degrees for Positivstellensatz and Hilbert 17-th problem, which is the expression of a nonnegative polynomial as a sum of squares of rational functions. We obtain a tower of five exponentials. A precise bound in terms of the number and degree of the polynomials and their number of variables is provided in the paper.
Cite
@article{arxiv.1404.2338,
title = {An elementary recursive bound for effective Positivstellensatz and Hilbert 17-th problem},
author = {Henri Lombardi and Daniel Perrucci and Marie-Françoise Roy},
journal= {arXiv preprint arXiv:1404.2338},
year = {2017}
}