RT Journal Article
T1 Nonsingular systems of generalized Sylvester equations: An algorithmic approach
A1 Terán Vergara, Fernando de
A1 Iannazzo, Bruno
A1 Poloni, Federico
A1 Rebol, Leonardo
AB We 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.
PB John Wiley & Sons
SN 1070-5325
YR 2019
FD 2019-01-01
LK https://hdl.handle.net/10016/31725
UL https://hdl.handle.net/10016/31725
LA eng
NO Ministerio de Economía y Competitividad of Spain. Grant Numbers: MTM2015-68805-REDT, MTM2015- 65798-P; Istituto Nazionale di Alta Matematica “Francesco Severi”. Grant Number: GNCS Project 2016; Research project of the Università di Perugia Soluzione numerica di problemi di algebra lineare strutturata
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RD 17 jun. 2024