We prove that multilinear (tensor) analogues of many efficiently computable problems in
numerical linear algebra are NP-hard. Our list includes: determining the feasibility of a …

We show that for several notions of rank including tensor rank, Waring rank, and generalized
rank with respect to a projective variety, the maximum value of rank is at most twice the …

We consider here the problem, which is quite classical in Algebraic geometry, of studying
the secant varieties of a projective variety X. The case we concentrate on is when X is a …

A Waring decomposition of a polynomial is an expression of the polynomial as a sum of
powers of linear forms, where the number of summands is minimal possible. We prove that …

We prove a conjecture of Comon and Ottaviani that typical real Waring ranks of bivariate
forms of degree d take all integer values between ⌊d+22⌋ and d. That is, we show that for …

Comon's Conjecture claims that for a symmetric tensor, its rank and its symmetric rank
coincide. We show that this conjecture is true under an additional assumption that the rank …

We introduce a convergent hierarchy of lower bounds on the minimum value of a real form
over the unit sphere. The main practical advantage of our hierarchy over the real sum-of …

MONOMIALS AS SUMS OF POWERS: THE REAL BINARY CASE 1. Introduction It is well-known,
and easy to prove, that if k is a field of c Page 1 PROCEEDINGS OF THE AMERICAN …

On the real rank of monomials | SpringerLink Skip to main content Advertisement SpringerLink
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In what follows, we pose two general conjectures about decompositions of homogeneous
polynomials as sums of powers. The first one (suggested by G. Ottaviani) deals with the …