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Nonsingular systems of generalized Sylvester equations: An algorithmic approach

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dc.affiliation.dptoUC3M. Departamento de Matemáticases
dc.affiliation.grupoinvUC3M. Grupo de Investigación: Matemática Aplicada a Control, Sistemas y Señaleses
dc.contributor.authorTerán Vergara, Fernando de
dc.contributor.authorIannazzo, Bruno
dc.contributor.authorPoloni, Federico
dc.contributor.authorRebol, Leonardo
dc.contributor.funderMinisterio de Economía y Competitividad (España)es
dc.date.accessioned2021-01-19T11:29:09Z
dc.date.available2021-01-19T11:29:09Z
dc.date.issued2019-01-01
dc.description.abstractWe 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.en
dc.description.sponsorshipMinisterio 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 strutturataen
dc.identifier.bibliographicCitationDe Terán, F, Iannazzo, B, Poloni, F, Robol, L. Nonsingular systems of generalized Sylvester equations: An algorithmic approach. Numer Linear Algebra Appl. 2019; 26:e2261
dc.identifier.doihttps://doi.org/10.1002/nla.2261
dc.identifier.issn1070-5325
dc.identifier.publicationissue5
dc.identifier.publicationtitleNumer Linear Algebra with Applications
dc.identifier.publicationvolume26
dc.identifier.urihttps://hdl.handle.net/10016/31725
dc.identifier.uxxiAR/0000024546
dc.language.isoeng
dc.publisherJohn Wiley & Sons
dc.relation.projectIDGobierno de España. MTM2015-68805-REDTes
dc.relation.projectIDGobierno de España. MTM2015- 65798-Pes
dc.rights© 2019 John Wiley & Sons, Ltd.
dc.rights.accessRightsopen access
dc.subject.ecienciaMatemáticases
dc.subject.otherFormal matrix producten
dc.subject.otherMatrix pencilsen
dc.subject.otherPeriodic QR/QZ algorithmen
dc.subject.otherPeriodic Schur decompositionen
dc.subject.otherSylvester and ⋆‐Sylvester equationsen
dc.subject.otherSystems of linear matrix equationsen
dc.titleNonsingular systems of generalized Sylvester equations: An algorithmic approachen
dc.typeresearch article*
dc.type.hasVersionAM*
dspace.entity.typePublication
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