Communication cost of sparse Cholesky factorization on a hypercube
The authors consider the nested dissection ordering of a k x k grid of nodes and the Cholesky factorization of the associated k squared x k squared symmetric matrix. When the factorization is computed on a hypercube machine with p processors, then the communication cost (the total number of nonzero elements that need to be communicated among the processors) can be kept down to O (pk squared) when the processors are assigned appropriately. This result was proved in George, Liu and Ng (1987). The authors offer a simple proof of a slightly stronger result: the communication cost for each processor is O (k squared). Load balancing is built into the proof. Their argument extends to grids in more than 2 dimensions.
- Research Organization:
- California Univ., Berkeley, CA (USA). Center for Pure and Applied Mathematics
- OSTI ID:
- 5754944
- Report Number(s):
- AD-A-206860/9/XAB; PAM-436
- Country of Publication:
- United States
- Language:
- English
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