{"ID":2870719,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.11540","arxiv_id":"2509.11540","title":"Positive Definiteness and Stability of Interval Tensors","abstract":"In this paper, we focus on the positive definiteness and Hurwitz stability of interval tensors. First, we introduce auxiliary tensors $\\mathcal{A}^z$ and establish equivalent conditions for the positive (semi-)definiteness of interval tensors. That is, an interval tensor is positive definite if and only if all $\\mathcal{A}^z$ are positive (semi-)definite. For Hurwitz stability, it is revealed that the stability of the symmetric interval tensor $\\mathcal{A}_s^I$ can deduce the stability of the interval tensor $\\mathcal{A}^I$, and the stability of symmetric interval tensors is equivalent to that of auxiliary tensors $\\tilde{\\mathcal{A}}^z$. Finally, taking $4$th order $3$-dimensional interval tensors as examples, the specific sufficient conditions are built for their positive (semi-)definiteness.","short_abstract":"In this paper, we focus on the positive definiteness and Hurwitz stability of interval tensors. First, we introduce auxiliary tensors $\\mathcal{A}^z$ and establish equivalent conditions for the positive (semi-)definiteness of interval tensors. That is, an interval tensor is positive definite if and only if all $\\mathca...","url_abs":"https://arxiv.org/abs/2509.11540","url_pdf":"https://arxiv.org/pdf/2509.11540v1","authors":"[\"Li Ye\",\"Yisheng Song\"]","published":"2025-09-15T03:16:01Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}