Abstract
Several relative eigenvalue condition numbers that exploit tridiagonal form are derived. Some of them use triangular factorizations instead of the matrix entries and so they shed light on when eigenvalues are less sensitive to perturbations of factored forms than to perturbations of the matrix entries. A novel empirical condition number is used to show when perturbations are so large that the eigenvalue response is not linear. Some interesting examples are examined in detail.
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C. Ferreira is supported by FEDER Funds through “Programa Operacional Factores de Competitividade: COMPETE” and by Portuguese Funds through FCT: “Fundação para a Ciência e a Tecnologia”, within the Project PEst-C/MAT/UI0013/2011. The research of F. Dopico was partially supported by the Ministerio de Ciencia e Innovación of Spain through the research grant MTM-2009-09281.
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Ferreira, C., Parlett, B. & Dopico, F.M. Sensitivity of eigenvalues of an unsymmetric tridiagonal matrix. Numer. Math. 122, 527–555 (2012). https://doi.org/10.1007/s00211-012-0470-z
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DOI: https://doi.org/10.1007/s00211-012-0470-z