Parallel Block Matrix Factorizations on the Shared-Memory Multiprocessor Ibm 3090 VF/600J

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Abstract
Efficient parallel block algorithms for the LU factorization with partial pivoting, the Cholesky factorization, and the QR factorization transportable over a range of parallel MIMD architectures are presented. Parallel implementations of different block algorithms that utilize optimized uniprocessor level-3 BLAS are compared with corresponding routines of LAPACK (under development). Parallelism is mainly invoked implicitly in LAPACK by replacing calls to uniprocessor level-3 kernels by calls to parallel level-3 kernels and thereby maintaining portability. However, by parallelizing at the block level (explicitly) it is possible to overlap and pipeline different matrix-matrix operations and thereby gain some performance. Theoretical models give upper bounds on the best possible speedup of the explicitly and implicitly parallel block algorithms for the target machine.

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