Summary
The development of a new parallel algorithm performing the LU-decomposition of a regular matrix is given. The algorithm is developed using formal techniques that rely on the use of invariants that express the properties of parallel processes (like in the Gries-Owicki approach) and ordered sets that define the communications between them. Special attention is given to the new notion of a parallel invariant: it is made clear that many invariants contain too many implicit sequential constraints, which makes them inferior to other ones. Also considered are the efficiency, both in communications and in computations, and the correctness. It is shown that the algorithm suggested in this paper has better efficiency than algorithms that use a partitioning of the matrix into rows, columns, or blocks. The programming techniques used are evaluated against the programming demands posed by the specific problem considered.
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van de Vorst, J.G.G. The formal development of a parallel program performing LU-decomposition. Acta Informatica 26, 1–17 (1988). https://doi.org/10.1007/BF02915443
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DOI: https://doi.org/10.1007/BF02915443