Subcube matrix decomposition: A unifying view for LU factorization on multicomputers

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