Matrix computations (3rd ed.)
ScaLAPACK user's guide
Gossip-Based Computation of Aggregate Information
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Distributed optimization in sensor networks
Proceedings of the 3rd international symposium on Information processing in sensor networks
A decentralized algorithm for spectral analysis
Journal of Computer and System Sciences
Broadcast gossip algorithms for consensus
IEEE Transactions on Signal Processing
ICT'09 Proceedings of the 16th international conference on Telecommunications
Parallel tiled QR factorization for multicore architectures
PPAM'07 Proceedings of the 7th international conference on Parallel processing and applied mathematics
Scalable Tile Communication-Avoiding QR Factorization on Multicore Cluster Systems
Proceedings of the 2010 ACM/IEEE International Conference for High Performance Computing, Networking, Storage and Analysis
Energy-Aware Distributed QR Decomposition on Wireless Sensor Nodes
The Computer Journal
IEEE Transactions on Information Theory
Hierarchical Cooperation Achieves Optimal Capacity Scaling in Ad Hoc Networks
IEEE Transactions on Information Theory
Robust distributed orthogonalization based on randomized aggregation
Proceedings of the second workshop on Scalable algorithms for large-scale systems
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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.