Elias' Article

Bounds on real eigenvalues and singular values of interval matrices.
Milan Hlad\'ik, David Daney, and Elias P. Tsigaridas.
SIAM Journal of Matrix Analysis and Applications, 31(4):2116–2129, 2010.

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Abstract:

We study bounds on real eigenvalues of interval matrices, and our aim is to develop fast computable formulae that produce as-sharp-as-possible bounds. We consider two cases: general and symmetric interval matrices. We focus on the latter case, since on one hand such interval matrices have many applications in mechanics and engineering, and on the other many results from classical matrix analysis could be applied to them. We also provide bounds for the singular values of (generally non-square) interval matrices. Finally, we illustrate and compare the various approaches by a series of examples.

@Article{hdt-simax-2010,
  author =       {Milan Hlad{\'i}k and David Daney and Elias
                  P. Tsigaridas},
  title =        {Bounds on real eigenvalues and singular values of
                  interval matrices},
  journal =      {SIAM Journal of Matrix Analysis and Applications},
  volume =       31,
  number =       4,
  pages =        {2116-2129},
  keywords =     {interval matrix; interval analysis; real eigenvalue;
                  eigenvalue bounds; singular value},
  year =         2010,
  abstract =     " We study bounds on real eigenvalues of interval
                  matrices, and our aim is to develop fast computable
                  formulae that produce as-sharp-as-possible
                  bounds. We consider two cases: general and symmetric
                  interval matrices.  We focus on the latter case,
                  since on one hand such interval matrices have many
                  applications in mechanics and engineering, and on
                  the other many results from classical matrix
                  analysis could be applied to them. We also provide
                  bounds for the singular values of (generally
                  non-square) interval matrices. Finally, we
                  illustrate and compare the various approaches by a
                  series of examples. ",
}

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