Factoring Dense And Sparse Matrices
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In the last two chapters the effects of the data dependencies on the computation time and the communication requirements of some uniform and regular dags are discussed. All the vertices in any of the dags considered have identical data dependency structure. In general, if a dag does not have uniform data dependencies, it is difficult to systematically study and compare the effects on the overall performance of different partitioning and scheduling schemes. In many instances, however, there is some regularity in the data dependency structure that can be exploited in analyzing the computation time and the associated data traffic. This is demonstrated in this chapter by considering the problem of computing the factorization of dense and sparse matrices. To keep the discussion simple, only symmetric positive definite matrices are considered.
KeywordsShared Memory Data Traffic Sparse Matrix Assignment Scheme Cholesky Factorization
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