Parallel Sparse Triangular Solution with Partitioned Inverses and Prescheduled Dags
نویسندگان
چکیده
Sparse triangular solution ooers a challenging irregular problem for parallel systems. The repeated solution of the system Lx = b, where L is a lower triangular factor of a sparse matrix, arises in numerous applications. A previous study 1] has shown that, if L is an incomplete factor, Lx = b can be eeciently solved on a parallel system through substitution. This was accomplished by representing the computation as a directed acyclic graph (DAG) that was prescheduled by dominant sequence clustering (DSC) 2]. Unfortunately, when L is a complete factor, paral-lelism is extremely limited. This study uses the method of partitioned inverses 3] 4] to increase available par-allelism over substitution, commonly by an order of magnitude. We also represent our partitioned inverses computation as a DAG and preschedule using DSC. Our preliminary results exhibit dramatically improved speedups on the CM5 and CM5E.
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