Highly parallel sparse Cholesky factorization
The paper develops and compares several fine-grained parallel algorithms to compute the Cholesky factorization of a sparse matrix. The experimental implementations are on the Connection Machine, a distributed-memory SIMD machine whose programming model conceptually supplies one processor per data element. In contrast to special-purpose algorithms in which the matrix structure conforms to the connection structure of the machine, the focus is on matrices with arbitrary sparsity structure. The most promising algorithm is one whose inner loop performs several dense factorizations simultaneously on a two-dimensional grid of processors. Virtually any massively parallel dense factorization algorithm can be used as the key subroutine. The sparse code attains execution rates comparable to those of the dense subroutine. It also presents a performance model and uses it to analyze the algorithms. It finds that asymptotic analysis combined with experimental measurement of parameters is accurate enough to be useful in choosing among alternative algorithms for a complicated problem.
- Research Organization:
- Xerox Palo Alto Research Center, CA (USA). Systems Sciences Lab.
- OSTI ID:
- 6204789
- Report Number(s):
- PB-91-111724/XAB; CSL--90-7
- Country of Publication:
- United States
- Language:
- English
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