@Article{Lee:2008:AET,
  author =       "Che-Rung Lee and G. W. Stewart",
  title =        "Algorithm 879: {EIGENTEST}: A Test Matrix Generator for Large-Scale Eigenproblems",
  journal =      "{ACM} Transactions on Mathematical Software",
  volume =       "35",
  number =       "1",
  month =        jul,
  year =         "2008",
  pages =        "7:1--7:11",
  URL =          "http://doi.acm.org/10.1145/1377603.1377610",
  abstract =     "EIGENTEST is a package that produces real test matrices with known eigensystems.  A test 
                 matrix, called an eigenmat, is generated in a factored form, in which the user can specify the 
                 eigenvalues and has some control over the condition of the eigenvalues and eigenvectors.
                 An eigenmat $A$ of order $n$ requires only $O(n)$ storage for its representation.  Auxiliary 
                 programs permit the computation of $(A - sI)b$, $(A - s I)^{\rm -T} b$, $(A - s I)^{-1} b$, 
                 and $(A - s I)^{\rm -T}b$ in $O(n)$ operations.  A special routine computes specified eigenvectors
                 of an eigenmat and the condition of its eigenvalue.  Thus eigenmats are suitable for testing 
                 algorithms based on Krylov sequences, as well as others based on matrix-vector products.  This 
                 paper introduces the eigenmat and describes implementations in Fortran~77, Fortran~95, C, and Matlab.",
}