Elias' Article

An algorithm for addressing the real interval eigenvalue problem.
Milan Hladík, David Daney, and Elias P. Tsigaridas.
J. Comput. Appl. Math., 235(8):2715–2730, 2011.

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Abstract:

In this paper we present an algorithm for approximating the range of the real eigenvalues of interval matrices. Such matrices could be used to model real-life problems, where data sets suffer from bounded variations such as uncertainties (e.g. tolerances on parameters, measurement errors), or to study problems for given states. The algorithm that we propose is a subdivision algorithm that exploits sophisticated techniques from interval analysis. The quality of the computed approximation and the running time of the algorithm depend on a given input accuracy. We also present an efficient C++ implementation and illustrate its efficiency on various data sets. In most of the cases we manage to compute efficiently the exact boundary points (limited by floating point representation).

@article{hdt-jcam-2011,
  author =       "Milan Hlad\'{\i}k and David Daney and
                  Elias~P. Tsigaridas",
  title =        "An algorithm for addressing the real interval
                  eigenvalue problem",
  journal =      "J. Comput. Appl. Math.",
  fjournal =     "Journal of Computational and Applied Mathematics",
  volume =       235,
  number =       8,
  pages =        "2715-2730",
  year =         2011,
  abstract =     "In this paper we present an algorithm for
                  approximating the range of the real eigenvalues of
                  interval matrices. Such matrices could be used to
                  model real-life problems, where data sets suffer
                  from bounded variations such as uncertainties
                  (e.g. tolerances on parameters, measurement errors),
                  or to study problems for given states. The algorithm
                  that we propose is a subdivision algorithm that
                  exploits sophisticated techniques from interval
                  analysis. The quality of the computed approximation
                  and the running time of the algorithm depend on a
                  given input accuracy. We also present an efficient
                  C++ implementation and illustrate its efficiency on
                  various data sets. In most of the cases we manage to
                  compute efficiently the exact boundary points
                  (limited by floating point representation).",
  keywords =     "interval matrix, real eigenvalue, eigenvalue bounds,
                  regularity, interval analysis",
}

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