author: | Clémentin Tayou Djamegni |
---|---|
title: | Synthesis Of Space-Time Optimal Systolic Algorithms For The Cholesky Factorization |
keywords: | parallel processing, projection methods, timing function, allocation function, space-time complexity, re-indexation |
abstract: | In this paper we study the synthesis of space-time optimal
systolic arrays for the Cholesky Factorization (CF). First, we discuss
previous allocation methods and their application to CF. Second, stemming from
a new allocation method we
derive a space-time optimal array, with nearest neighbor
connections, that requires 3N + Θ(1) time steps and N2/8 + Θ(N)
processors, where N is the size of the problem. The number of processors
required by this new design improves the best previously known bound,
N2/6 + Θ(N), induced by previous allocation methods.
This is the first contribution of the paper.
The second contribution stemms from the fact that the paper also introduces
a new allocation method that suggests to first perform
index transformations on the initial dependence graph of a given system of
uniform recurrent equations before
applying the weakest allocation method, the projection method.
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reference: | Clémentin Tayou Djamegni (2002), Synthesis Of Space-Time Optimal Systolic Algorithms For The Cholesky Factorization, Discrete Mathematics and Theoretical Computer Science 5, pp. 109-120 |
bibtex: | For a corresponding BibTeX entry, please consider our BibTeX-file. |
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