Terán Vergara, Fernando deIannazzo, BrunoPoloni, FedericoRebol, Leonardo2021-01-192021-01-192019-01-01De Terán, F, Iannazzo, B, Poloni, F, Robol, L. Nonsingular systems of generalized Sylvester equations: An algorithmic approach. Numer Linear Algebra Appl. 2019; 26:e22611070-5325https://hdl.handle.net/10016/31725We consider the uniqueness of solution (i.e., nonsingularity) of systems of r generalized Sylvester and ⋆‐Sylvester equations with n×n coefficients. After several reductions, we show that it is sufficient to analyze periodic systems having, at most, one generalized ⋆‐Sylvester equation. We provide characterizations for the nonsingularity in terms of spectral properties of either matrix pencils or formal matrix products, both constructed from the coefficients of the system. The proposed approach uses the periodic Schur decomposition and leads to a backward stable O(n3r) algorithm for computing the (unique) solution.eng© 2019 John Wiley & Sons, Ltd.Formal matrix productMatrix pencilsPeriodic QR/QZ algorithmPeriodic Schur decompositionSylvester and ⋆‐Sylvester equationsSystems of linear matrix equationsresearch articleMatemáticashttps://doi.org/10.1002/nla.2261open access5Numer Linear Algebra with Applications26AR/0000024546