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

Clémentin Tayou Djamegni (1)

1 Laboratoire d'Informatique [Dschang]

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.

Mots clés: parallel processing; projection methods; timing function; allocation function; space-time complexity; re-indexation

Domaines: Mathématique discrète [cs.DM]

Clémentin Tayou Djamegni. Synthesis of space-time optimal systolic algorithms for the Cholesky factorization. Discrete Mathematics and Theoretical Computer Science, 2002, Vol. 5, pp.109-120. ⟨10.46298/dmtcs.305⟩. ⟨hal-00958976⟩