Bibliographic record for `Davis:2008:DSS'

@Article{Davis:2008:DSS,
  author =       "Timothy A. Davis and William W. Hager",
  title =        "Dynamic Supernodes in Sparse {Cholesky} Update/downdate and Triangular Solves",
  journal =      "{ACM} Transactions on Mathematical Software",
  volume =       "35",
  number =       "4",
  accepted =     "2 May 2008",
  upcoming =     "true",
  abstract =     "The supernodal method for sparse Cholesky factorization represents the factor $L$ as a set of supernodes, each 
                 consisting of a contiguous set of columns of $L$ with identical nonzero pattern.  A conventional supernode is stored as 
                 a dense submatrix.  While this is suitable for sparse Cholesky factorization where the nonzero pattern of $L$ does not 
                 change, it is not suitable for methods that modify a sparse Cholesky factorization after a low-rank change to $A$ (an 
                 update/downdate, $\overline{A} = A \pm WW^T$). Supernodes merge and split apart during an update/downdate. Dynamic 
                 supernodes are introduced, which allow a sparse Cholesky update/downdate to obtain performance competitive with 
                 conventional supernodal methods.  A dynamic supernodal solver is shown to exceed the performance of the conventional 
                 (BLAS-based) supernodal method for solving triangular systems.  These methods are incorporated into CHOLMOD, a sparse
                 Cholesky factorization and update/downdate package, which forms the basis of \verb'x=A\b' in MATLAB when \verb'A' is 
                 sparse and symmetric positive definite.",
}