Abstract
Most parallel algorithms for matrix computations assume a static network with reliable communication and thus use fixed communication schedules. However, in situations where computer systems may change dynamically, in particular, when they have unreliable components, algorithms with randomized communication schedule may be an interesting alternative.
We investigate randomized algorithms based on gossiping for the distributed computation of the QR factorization. The analyses of numerical accuracy showed that known numerical properties of classical sequential and parallel QR decomposition algorithms are preserved. Moreover, we illustrate that the randomized approaches are well suited for distributed systems with arbitrary topology and potentially unreliable communication, where approaches with fixed communication schedules have major drawbacks. The communication overhead compared to the optimal parallel QR decomposition algorithm (CAQR) is analyzed. The randomized algorithms have a much higher potential for trading off numerical accuracy against performance because their accuracy is proportional to the amount of communication invested.
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Straková, H., Gansterer, W.N., Zemen, T. (2012). Distributed QR Factorization Based on Randomized Algorithms. In: Wyrzykowski, R., Dongarra, J., Karczewski, K., Waśniewski, J. (eds) Parallel Processing and Applied Mathematics. PPAM 2011. Lecture Notes in Computer Science, vol 7203. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31464-3_24
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DOI: https://doi.org/10.1007/978-3-642-31464-3_24
Publisher Name: Springer, Berlin, Heidelberg
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