Discrete Mathematics & Theoretical Computer Science, Vol 5 (2002)

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DMTCS vol 5 no 1 (2002), pp. 109-120

Discrete Mathematics & Theoretical Computer Science


Volume 5 n° 1 (2002), pp. 109-120

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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