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The explicit formula for Gauss-Jordan elimination applied to flexible systems

2022Journal article Open access
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dc.contributor.authorTran, Nam van
dc.contributor.authorJustino, Júlia
dc.contributor.authorBerg, Imme van den
dc.date.accessioned2022-06-15T11:14:19Z
dc.date.available2022-06-15T11:14:19Z
dc.date.issued2022
dc.description.abstractFlexible systems are obtained from systems of linear equations by adding to the elements of the coefficient matrix and the right-hand side scalar neutrices, which are convex groups of (non-standard) real numbers. The neutrices model imprecisions, giving rise to calculation rules extending informal error calculus. Stability conditions for flexible systems are given in terms of relative imprecision and size of determinants. We then apply the explicit formula for the elements of the successive intermediate matrices of the Gauss-Jordan elimination procedure to find the solution of flexible systems, keeping track of the error terms at every stage. The solution respects the original imprecisions in the right-hand side and is the same as the one given by Cramer’s rule.pt_PT
dc.description.versioninfo:eu-repo/semantics/publishedVersionpt_PT
dc.identifier.citationTran, N., Justino, J. & Berg, I. (2022). The explicit formula for Gauss-Jordan elimination applied to flexible systems. Special Matrices, 10(1), 366-393. https://doi.org/10.1515/spma-2022-0168 Copy to clipboard BIBTEpt_PT
dc.identifier.doi10.1515/spma-2022-0168pt_PT
dc.identifier.issn2300-7451
dc.identifier.urihttp://hdl.handle.net/10400.26/41075
dc.language.isoengpt_PT
dc.peerreviewedyespt_PT
dc.subjectGauss-Jordan eliminationpt_PT
dc.subjectFlexible systemspt_PT
dc.subjectStabilitypt_PT
dc.subjectExternal numberspt_PT
dc.titleThe explicit formula for Gauss-Jordan elimination applied to flexible systemspt_PT
dc.typejournal article
dspace.entity.typePublication
person.familyNameda Rocha Vilaverde Justino
person.givenNameJúlia Maria
person.identifier.ciencia-id271A-0DFC-B336
person.identifier.orcid0000-0002-7526-6247
rcaap.rightsopenAccesspt_PT
rcaap.typearticlept_PT
relation.isAuthorOfPublication64f60ae1-fcf2-45b2-8a62-58b6d06ab068
relation.isAuthorOfPublication.latestForDiscovery64f60ae1-fcf2-45b2-8a62-58b6d06ab068

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