The supernodal method for sparse Cholesky factorization represents the factor
Las a set of supernodes, each consisting of a contiguous set of columns of Lwith 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 Ldoes not change, it is not suitable for methods that modify a sparse Cholesky factorization after a low-rank change to A(an update/downdate, = A WWT ). 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 x = A\b MATLAB when A is sparse and symmetric positive definite.