Showing 379–392 of 7,997 results for "Bidoli Ettore"

Journals 2024 EN

Generalized identifiability of sums of squares

Giorgio Ottaviani · Ettore Teixeira Turatti

Let $f$ be a homogeneous polynomial of even degree $d$. We study thedecompositions $f=\sum_{i=1}^r f_i^2$ where $\mathrm{deg} f_i=d/2$. The minimalnumber of summands $r$ is called the $2$-rank of $f$, so that the polynomialshaving $2$-rank equal to $1$ are exactly the squares. Such decompositions arenever unique and they are divided into $\mathrm{O}(r)$-orbits, the problembecomes counting how many different $\mathrm{O}(r)$-orbits of decompositionexist. We say that $f$ is $\mathrm{O}(r)$-identifiable if there is a unique$\mathrm{O}(r)$-orbit. We give sufficient conditions for generic and specific$\mathrm{O}(r)$-identifiability. Moreover, we show the generic$\mathrm{O}(r)$-identifiability of ternary forms.

Elsevier BV