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TitleThe inverse eigenvector problem for real tridiagonal matrices
Author(s)Parlett, Beresford
Dopico, Froilán M.
Ferreira, Carla
KeywordsBackward errors
Tridiagonal matrices
Issue date27-Apr-2016
PublisherSociety for Industrial and Applied Mathematics
JournalSIAM Journal on Matrix Analysis and Applications
Abstract(s)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.
Publisher version
AccessOpen access
Appears in Collections:CMAT - Artigos em revistas com arbitragem / Papers in peer review journals

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