The Inverse Eigenvector Problem for Real Tridiagonal Matrices

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dc.contributor.author Parlett, Beresford
dc.contributor.author Martínez Dopico, Froilán César
dc.contributor.author Ferreira, Carla
dc.date.accessioned 2021-03-18T09:14:26Z
dc.date.available 2021-03-18T09:14:26Z
dc.date.issued 2016
dc.identifier.bibliographicCitation Parlett, B., Dopico, F. M., Ferreira, C. (2016). The Inverse Eigenvector Problem for Real Tridiagonal Matrices. SIAM Journal on Matrix Analysis and Applications, 37(2), pp. 577–597.
dc.identifier.issn 0895-4798
dc.identifier.uri http://hdl.handle.net/10016/32168
dc.description.abstract A little known property of a pair of eigenvectors (column and row) of a real tridiagonal matrix is presented. With its help we can define necessary and sufficient conditions for the unique real tridiagonal matrix for which an approximate pair of complex eigenvectors is exact. Similarly, we can designate the unique real tridiagonal matrix for which two approximate real eigenvectors, with different real eigenvalues, are also exact. We close with an illustration that these unique "backward error" matrices are sensitive to small rounding errors in certain partial sums which play a key role in determining the matrices.
dc.format.extent 21
dc.language.iso eng
dc.publisher Society for Industrial and Applied Mathematics (SIAM)
dc.rights © 2016, Society for Industrial and Applied Mathematics
dc.subject.other Backward errors
dc.subject.other Tridiagonal matrices
dc.subject.other Eigenvector
dc.subject.other Eigenvalue problems
dc.title The Inverse Eigenvector Problem for Real Tridiagonal Matrices
dc.type article
dc.subject.eciencia Matemáticas
dc.identifier.doi https://doi.org/10.1137/15M1025293
dc.rights.accessRights openAccess
dc.relation.projectID Gobierno de España. MTM2012-32542
dc.type.version acceptedVersion
dc.identifier.publicationfirstpage 577
dc.identifier.publicationissue 2
dc.identifier.publicationlastpage 597
dc.identifier.publicationtitle SIAM Journal on Matrix Analysis and Applications
dc.identifier.publicationvolume 37
dc.identifier.uxxi AR/0000018401
dc.contributor.funder Ministerio de Economía y Competitividad (España)
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