CISE Submissions

Item: REP-2006-109

Item:REP-2006-109

Title:Dynamic supernodes in sparse Cholesky update/downdate and triangular solves

Timothy A. Davis
William W. Hager

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, A = A +/- 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 x=A in MATLAB when A is sparse and symmetric positive definite.

Supporting File:here

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