{"ID":2865990,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.21101","arxiv_id":"2509.21101","title":"On structured condition number of rational matrix functions","abstract":"We derive the necessary and sufficient conditions for the simple eigenvalues of rational matrix functions with symmetry structure to have the same normwise condition number with respect to arbitrary and structure-preserving perturbations. We obtain an exact expression for the structured condition number of simple eigenvalues of symmetric, skew-symmetric and even/odd rational matrix functions, and tight bounds are obtained for simple eigenvalues of Hermitian, skew-Hermitian, even/odd, and palindromic rational matrix functions.","short_abstract":"We derive the necessary and sufficient conditions for the simple eigenvalues of rational matrix functions with symmetry structure to have the same normwise condition number with respect to arbitrary and structure-preserving perturbations. We obtain an exact expression for the structured condition number of simple eigen...","url_abs":"https://arxiv.org/abs/2509.21101","url_pdf":"https://arxiv.org/pdf/2509.21101v1","authors":"[\"Ritwik Prabin Kalita\",\"Anshul Prajapati\",\"Punit Sharma\"]","published":"2025-09-25T12:47:21Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}