Istituto di Scienza e Tecnologie dell'Informazione     
Codenotti B., Leoncini M., Resta G. Solving general linear systems in parallel. In: International Symposium on Computer and Information Sciences VII. (Antalya, Turkey, 4 - 6 November 1992). Proceedings, pp. 17 - 23. Erol Gelenbe, Ugur Halici, Neşe Ylabik (eds.). Presses de l'EHEI, Université René Descartes, 1992.
In this paper we present two algorithms for parallel matrix inversion and related problems which are competitive with the best methods known so far. Our first algorithm is a generalization of Csanky's algorithm. It is based on a polynomial preconditioning technique and achieves, for general n x n matrices with minimum polynomial of degree m, O (log n log m) parallel time bound. Our second algorithm is based on an iterative computation scheme, called reapeated matrix squaring. For well-conditioned matrices it is characterized by time bounds ranging from 0 (log n) to O (log∆2 n). A nice feature of our algorithm is that it does not require the computation of an approximate inverse to be used as the starting point.

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