@Article{Gardiner:1992:SSM,
  author =       "Judith D. Gardiner and Alan J. Laub and James J. Amato
                 and Cleve B. Moler",
  title =        "Solution of the {Sylvester} Matrix Equation
                 {$AXB^{\sc{T}}+CXD^{\sc{T}}=E$}",
  journal =      "{ACM} Transactions on Mathematical Software",
  volume =       "18",
  number =       "2",
  pages =        "223--231",
  month =        jun,
  year =         "1992",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500",
  MRclass =      "65F05 (65-04 65F10 65F35)",
  MRnumber =     "1 167 892",
  URL =          "http://doi.acm.org/10.1145/146847.146929",
  abstract =     "A software package has been developed to solve
                 efficiently the Sylvester-type matrix equation $AXB^{T}
                 + CXD^{T} = E$. A transformation method is used which
                 employs the QZ algorithm to structure the equation in
                 such a way that it can be solved columnwise by a back
                 substitution technique. The algorithm is an extension
                 of the Bartels-Stewart method and the Hessenberg-Schur
                 method. The numerical performance of the algorithms and
                 software is demonstrated by application to
                 near-singular systems.",
  keywords =     "algorithms; performance",
  subject =      "{\bf G.1.3}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Numerical Linear Algebra, Linear systems
                 (direct and iterative methods). {\bf G.1.3}:
                 Mathematics of Computing, NUMERICAL ANALYSIS, Numerical
                 Linear Algebra, Conditioning. {\bf G.4}: Mathematics of
                 Computing, MATHEMATICAL SOFTWARE, Algorithm analysis.
                 {\bf G.4}: Mathematics of Computing, MATHEMATICAL
                 SOFTWARE, Efficiency. {\bf G.4}: Mathematics of
                 Computing, MATHEMATICAL SOFTWARE, Reliability and
                 robustness. {\bf F.2.1}: Theory of Computation,
                 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY,
                 Numerical Algorithms and Problems, Computations on
                 matrices.",
}