arXiv subjects

Yuhuai Zhou

Publications and source records attributed to Yuhuai Zhou.

2 recordsLinked to original sources

arXiv2025

The Real Vanishing Ideals of Nuclear p-Norm Balls

We study the algebraic and geometric structure related to tensor nuclear norms. We show that the unit ball of the nuclear norm is the convex hull of an irreducible real variety and give an explicit description of its real vanishing ideal. As a consequence, we obtain a simple criterion to decide when a primary ideal is prime, and we use it to prove that the ideal of the nuclear 2-norm is real reduced and prime.

math.AG↗

arXiv2025

Low-Rank Tensor Recovery via Theta Nuclear p-Norm

We investigate the low-rank tensor recovery problem using a relaxation of the nuclear p-norm by theta bodies. We provide algebraic descriptions of the norms and compute their Gröbner bases. Moreover, we develop geometric properties of these bodies. Finally, our numerical results suggest that for $n\times\cdots\times n$ tensors, $m\geq O(n)$ measurements should be sufficient to recover low-rank tensors via theta body relaxation.

math.OC↗