@Article{Howell:2005:ABG,
  author =       "Gary W. Howell and Nadia Diaa",
  title =        "Algorithm 841: {BHESS}: {Gaussian} Reduction to a Similar 
                 Banded {Hessenberg} Form",
  journal =      "{ACM} Transactions on Mathematical Software",
  volume =       "31",
  number =       "1",
  month =        mar,
  year =         "2005",
  pages =        "166--185",
  URL =          "http://doi.acm.org/10.1145/1055531.1055539", 
  abstract =     "BHESS  uses Gaussian similarity transformations to reduce a general
                 real square matrix to similar upper Hessenberg form.  Multipliers 
                 are bounded in root mean square by a user-supplied parameter.  If 
                 the input matrix is not highly nonnormal and the user-supplied 
                 tolerance on multipliers is of a size greater than ten, the returned 
                 matrix usually has small upper bandwidth. In such a case, 
                 eigenvalues of the returned matrix can be determined by the 
                 bulge-chasing BR iteration or by Rayleigh quotient iteration. BHESS 
                 followed by BR iteration determines a complete spectrum in about 
                 one-fifth the time required for orthogonal reduction to Hessenberg 
                 form followed by QR iterations. The FORTRAN 77 code provided for 
                 BHESS runs efficiently on a cache-based architecture.",
}