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Numerical linear algebra on shared memory multiprocessors. (English) Zbl 0719.65013

Signal processing, scattering and operator theory, and numerical methods, Proc. Int. Symp. Math. Theory Networks Syst., MTNS, Vol. III, Amsterdam/Neth. 1989, Prog. Syst. Control Theory 5, 411-420 (1990).
Summary: [For the entire collection see Zbl 0712.00016.]
The development of parallel computers has had a significant impact on the design of algorithms in numerical linear algebra. For efficient utilization of these machines one needs to exploit parallelism and the vector capability of each processor. Most importantly one needs to manage the memory system properly. In particular, for shared memory multiprocessors in which memory is often hierarchically structured, algorithms have to be carefully designed in order to profit from the faster access times of caches, local, or cluster memories compared to that of the global memory. In this paper we present some new and important techniques for designing algorithms which allow both parallelism/vectorization as well as efficient utilization of hierarchical memory systems.

MSC:

65F05 Direct numerical methods for linear systems and matrix inversion
65F50 Computational methods for sparse matrices
65F10 Iterative numerical methods for linear systems
65Y05 Parallel numerical computation

Citations:

Zbl 0712.00016