Summary
We show that the greedy algorithm introduced in [1] and [5] to perform the parallel QR decomposition of a dense rectangular matrix of sizem×n is optimal. Then we assume thatm/n 2 tends to zero asm andn go to infinity, and prove that the complexity of such a decomposition is asymptotically2n, when an unlimited number of processors is available.
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Cosnard, M., Muller, J.M. & Robert, Y. Parallel QR decomposition of a rectangular matrix. Numer. Math. 48, 239–249 (1986). https://doi.org/10.1007/BF01389871
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DOI: https://doi.org/10.1007/BF01389871