SOS approximations of nonnegative polynomials via simple high degree perturbation
| dc.creator | Lasserre, Jean B. | |
| dc.creator | Netzer, Tim | |
| dc.date | 2005-10-21 | |
| dc.date.accessioned | 2026-07-07T06:47:45Z | |
| dc.date.available | 2026-07-07T06:47:45Z | |
| dc.description | We show that every real polynomial $f$ nonnegative on $[-1,1]^{n}$ can be approximated in the $l_{1}$-norm of coefficients, by a sequence of polynomials $\{f_{\ep r}\}$ that are sums of squares. This complements the existence of s.o.s. approximations in the denseness result of Berg, Christensen and Ressel, as we provide a very simple and \textit{explicit} approximation sequence. Then we show that if the Moment Problem holds for a basic closed semi-algebraic set $K_S\subset\R^n$ with nonempty interior, then every polynomial nonnegative on $K_S$ can be approximated in a similar fashion by elements from the corresponding preordering. Finally, we show that the degree of the perturbation in the approximating sequence depends on $ε$ as well as the degree and the size of coefficients of the nonnegative polynomial $f$, but not on the specific values of its coefficients. | |
| dc.description | 12 pages | |
| dc.identifier | https://arxiv.org/abs/math/0510456 | |
| dc.identifier | http://arxiv.org/abs/math/0510456 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/103757 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 12E05, 12Y05, 90C22, 44A60 | |
| dc.title | SOS approximations of nonnegative polynomials via simple high degree perturbation | |
| dc.type | text |