In this paper, we present a partial survey of the tools borrowed from tensor algebra, which
have been utilized recently in Statistics and Signal Processing. It is shown why the …

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 …

Introduction. An elementary argument shows that a non-negative poly nomial on the real line
can be represented as a sum of squares of polynomials. T prove that a non-negative …

Tensor decompositions are at the core of many blind source separation (BSS) algorithms,
either explicitly or implicitly. In particular, the canonical polyadic (CP) tensor decomposition …

There has been a resurgence of interest in classical invariant theory driven by several
factors: new theoretical developments; a revival of computational methods coupled with …

A symmetric tensor is a higher order generalization of a symmetric matrix. In this paper, we
study various properties of symmetric tensors in relation to a decomposition into a symmetric …

The study of positive polynomials brings together algebra, geometry and analysis. The
subject is of fundamental importance in real algebraic geometry when studying the …

Evidence is presented to suggest that, in three dimensions, spherical 6-designs with N
points exist for N= 24, 26,≥ 28; 7-designs for N= 24, 30, 32, 34,≥ 36; 8-designs for N= 36 …

Hilbert's 17th Problem asks whether a real positive semidefinite polynomial can be
expressed as a sum of squares of rational functions. Artin answered “yes” in the 1920's …

New mathematical insights and rigorous results are often gained through extensive
experimentation using numerical examples or graphical images and analyzing them. Today …