This paper represents the first attempt towards a decomposition-independent implementation of parallel algorithms for matrix computations. Main framework is the Subcube Matrix Decomposition, given in this work, that allows to view in a unifying way the most diffuse matrix decompositions on multicomputers. Its decomposition-independent properties extend, moreover, to the design of parallel algorithms, to their optimization, and to the performance analysis. We have verified all these characteristics by implementing an LU factorization meta-algorithm that unifies the known parallel programs and allows a decomposition-independent performance analysis both analytical and experimental.
Subcube matrix decomposition: A unifying view for LU factorization on multicomputers / M., Angelaccio; Colajanni, Michele. - In: PARALLEL COMPUTING. - ISSN 0167-8191. - STAMPA. - 20:(1994), pp. 257-270.
Subcube matrix decomposition: A unifying view for LU factorization on multicomputers
COLAJANNI, Michele
1994
Abstract
This paper represents the first attempt towards a decomposition-independent implementation of parallel algorithms for matrix computations. Main framework is the Subcube Matrix Decomposition, given in this work, that allows to view in a unifying way the most diffuse matrix decompositions on multicomputers. Its decomposition-independent properties extend, moreover, to the design of parallel algorithms, to their optimization, and to the performance analysis. We have verified all these characteristics by implementing an LU factorization meta-algorithm that unifies the known parallel programs and allows a decomposition-independent performance analysis both analytical and experimental.
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