A fully parallel algorithm for the symmetric eigenvalue problem
SIAM Journal on Scientific and Statistical Computing
Why functional programming matters
The Computer Journal - Special issue on Lazy functional programming
Performance studies of Id on the Monsoon dataflow system
Journal of Parallel and Distributed Computing - Special issue on dataflow and multithreaded architectures
Control of parallelism in the Manchester Dataflow Machine
Proceedings of the Functional Programming Languages and Computer Architecture
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We study the producer-consumer parallelism of Eigensolvers composed of a tridiagonalization function, a tridiagonal solver, and a matrix multiplication, written in the non-strict functional programming language Id. We verify the claim that non-strict functional languages allow the natural exploitation of this type of parallelism, in the framework of realistic numerical codes. We compare the standard top-down Dongarra-Sorensen solver with a new, bottom-up version. We show that this bottom-up implementation is much more space efficient than the top-down version. Also, we compare both versions of the Dongarra-Sorensen solver with the more traditional QL algorithm, and verify that the Dongarra-Sorensen solver is much more efficient, even when run in a serial mode. We show that in a non-strict functional execution model, the Dongarra-Sorensen algorithm can run completely in parallel with the Householder function. Moreover, this can be achieved without any change in the code components. We also indicate how the critical path of the complete Eigensolver can be improved.