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arXiv · 1404.2338

An elementary recursive bound for effective Positivstellensatz and Hilbert 17-th problem

Henri Lombardi·Daniel Perrucci·Marie-Françoise Roy
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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.

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Henri Lombardi, Daniel Perrucci, Marie-Françoise Roy. 2014-04-09. An elementary recursive bound for effective Positivstellensatz and Hilbert 17-th problem. https://arxiv.org/abs/1404.2338

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