@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",
  month =        feb,
  year =         2009,
  pages =        "27:1--27:23",
  URL =          "http://doi.acm.org/10.1145/1462173.1462176",
  accepted =     "2 May 2008",
  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.",
}