Skip to Main content Skip to Navigation
Journal articles

Synthesis of space-time optimal systolic algorithms for the Cholesky factorization

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 N^2/8 + 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, N^2/6 + 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 clever index transformations on the initial dependence graph of a given system of uniform recurrent equations before applying the weakest allocation method, the projection method.
Document type :
Journal articles
Complete list of metadata

Cited literature [35 references]  Display  Hide  Download

https://hal.inria.fr/hal-00958976
Contributor : Service Ist Inria Sophia Antipolis-Méditerranée / I3s <>
Submitted on : Thursday, March 13, 2014 - 4:55:37 PM
Last modification on : Thursday, November 29, 2018 - 11:38:07 AM
Long-term archiving on: : Friday, June 13, 2014 - 12:07:12 PM

File

dm050107.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-00958976, version 1

Collections

Citation

Clémentin Tayou Djamegni. Synthesis of space-time optimal systolic algorithms for the Cholesky factorization. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2002, 5, pp.109-120. ⟨hal-00958976⟩

Share

Metrics

Record views

138

Files downloads

813