@Article{Sadkane:2011:ASM,
  author =       "Miloud Sadkane and Ahmed Touhami",
  title =        "Algorithm 918: {specdicho}: A {MATLAB} program for the 
                  spectral dichotomy of regular matrix pencils",
  journal =      "{ACM} Transactions on Mathematical Software",
  volume =       38,
  number =       3,
  pages =        "21:1--21:13",
  url =          "http://doi.acm.org/10.1145/2168773.2168780",
  month =        apr,
  year =         2012,
  accepted =     "17 August 2011",
  abstract =     "
                 Given a regular matrix pencil $\lambda \Bm - \Am$
                 and a positively oriented contour $\gamma$ in the
                 complex plane, the spectral dichotomy methods applied to
                 $\lambda \Bm - \Am$ and $\gamma$ consist in determining
                 whether $\lambda \Bm - \Am$  possesses eigenvalues
                 on or in a neighborhood of $\gamma$.  When no such
                 eigenvalues exist, these methods compute iteratively
                 the spectral projector $\Pm$ onto the right deflating
                 subspace of $\lambda \Bm - \Am$ associated with  the
                 eigenvalues inside/outside $\gamma$.  The computation
                 of the projector is accompanied by the spectral
                 norm $\left\|\Hm\right\|$ of a Hermitian positive
                 definite matrix $\Hm$ called the {\it dichotomy
                 condition  number}, which indicates the numerical
                 quality of the spectral projector $\Pm$. The smaller
                 $\left\|\Hm\right\|$ is, the better this quality. This
                 paper presents a {\sc Matlab} program ({\tt specdicho})
                 implementing the main types of spectral dichotomy where
                 $\gamma$ is a circle,  an ellipse, the imaginary axis
                 or a parabola.",
}