Abstract
We present a new recursive algorithm for the QR factorization of an m by n matrix A. The recursion leads to an automatic variable blocking that allow us to replace a level 2 part in a standard block algorithm by level 3 operations. However, there are some additional costs for performing the updates which prohibits the efficient use of the recursion for large n. This obstacle is overcome by using a hybrid recursive algorithm that outperforms the LAPACK algorithm DGEQRF by 78% to 21% as m=n increases from 100 to 1000. A successful parallel implementation on a PowerPC 604 based IBM SMP node based on dynamic load balancing is presented. For 2, 3, 4 processors and m=n=2000 it shows speedups of 1.96, 2.99, and 3.92 compared to our uniprocessor algorithm.
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© 1998 Springer-Verlag Berlin Heidelberg
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Elmroth, E., Gustavson, F. (1998). New serial and parallel recursive QR factorization algorithms for SMP systems. In: Kågström, B., Dongarra, J., Elmroth, E., Waśniewski, J. (eds) Applied Parallel Computing Large Scale Scientific and Industrial Problems. PARA 1998. Lecture Notes in Computer Science, vol 1541. Springer, Berlin, Heidelberg . https://doi.org/10.1007/BFb0095328
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DOI: https://doi.org/10.1007/BFb0095328
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