An Elementary Recursive Bound for Effective Positivstellensatz and Hilbert's 17th Problem Paperback / softback
by Henri Lombardi, Daniel Perrucci, Marie-Francoise Roy
Part of the Memoirs of the American Mathematical Society series
Paperback / softback
Description
The authors prove an elementary recursive bound on the degrees for Hilbert's 17th problem.
More precisely they express a nonnegative polynomial as a sum of squares of rational functions and obtain as degree estimates for the numerators and denominators the following tower of five exponentials $ 2^{ 2^{ 2^{d^{4^{k}}} } } $ where $d$ is the number of variables of the input polynomial.
The authors' method is based on the proof of an elementary recursive bound on the degrees for Stengle's Positivstellensatz.
More precisely the authors give an algebraic certificate of the emptyness of the realization of a system of sign conditions and obtain as degree bounds for this certificate a tower of five exponentials, namely $ 2^{ 2^{\left(2^{\max\{2,d\}^{4^{k}}}+ s^{2^{k}}\max\{2, d\}^{16^{k}{\mathrm bit}(d)} \right)} } $ where $d$ is a bound on the degrees, $s$ is the number of polynomials and $k$ is the number of variables of the input polynomials.
Information
-
Available to Order - This title is available to order, with delivery expected within 2 weeks
- Format:Paperback / softback
- Pages:113 pages
- Publisher:American Mathematical Society
- Publication Date:30/04/2020
- Category:
- ISBN:9781470441081
Other Formats
- PDF from £76.50
Information
-
Available to Order - This title is available to order, with delivery expected within 2 weeks
- Format:Paperback / softback
- Pages:113 pages
- Publisher:American Mathematical Society
- Publication Date:30/04/2020
- Category:
- ISBN:9781470441081
