Geometria Complessa e Geometria Differenziale
Geometria Complessa e Geometria Differenziale
home | mail | papers | authors | news | seminars | events | open positions | login

S. Naldi

Nonnegative polynomials and their Carathéodory number

created by naldi on 16 Mar 2018
modified on 13 May 2020


Published Paper

Inserted: 16 mar 2018
Last Updated: 13 may 2020

Journal: Discrete Comput Geom
Volume: 51
Pages: 559–568
Year: 2014

ArXiv: 1209.3298 PDF
Links: Publisher page


In 1888 Hilbert showed that every nonnegative homogeneous polynomial with real coefficients of degree $2d$ in $n$ variables is a sum of squares if and only if $d=1$ (quadratic forms), $n=2$ (binary forms) or $(n,d)=(3,2)$ (ternary quartics). In these cases, it is interesting to compute canonical expressions for these decompositions. Starting from Carath\'eodory's Theorem, we compute the Carath\'eodory number of Hilbert cones of nonnegative quadratic and binary forms.

Credits | Cookie policy | HTML 5 | CSS 2.1