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QR Factorization of a Dense Matrix on a Hypercube Multiprocessor

In this article a new algorithm for computing the QR factorization of a rectangular matrix on a hypercube multiprocessor is described. The hypercube network is configured as a two-dimensional subcube-grid in the proposed scheme. A global communication scheme that uses redundant computation to maintain data proximity is employed, and the mapping strategy is such that for a fixed number of processors the processor idle time is small and either constant or grows linearly with the dimension of the matrix. A complexity analysis shows what the aspect ratio of the configured grid should be in terms of the shape of the matrix and the relative speeds of communication and computation. Numerical experiments performed on an Intel Hypercube multiprocessor support the theoretical results.