| 英文摘要 |
Solving large sparse symmetric and positive definite linear systems has been the core of many engineering and scientific computing problems. In direct solution of such a system of the form Ax = b, the coefficient matrix A is usually first decomposed into LLT, named as Cholesky factorization, where L is a lower triangular matrix. Since Cholesky factorization is computation-intensive, many researchers have pursued more efficient ways of performing the Cholesky factorization in parallel. One of these efforts involves finding and exploiting an appropriate ordering of the sparse matrix A to the parallelism inherent in the sparsity structure of A, as we ll as to keep the number of fill incurred during the factorization as small as possible. For general sparse symmetric and positive definite matrices, this problem is NP-hard. Jess and Kees propose a systematic way that decouples the process into two separate phases. The first phase uses a heuristic to find a fill reducing order and then the second phase finds a reordering that maximizes the parallelism of the factorization. |
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