Parallel variants of the multishift QZ algorithm with advanced deflation techniques
PARA'06 Proceedings of the 8th international conference on Applied parallel computing: state of the art in scientific computing
Dimensional analysis applied to a parallel QR algorithm
PPAM'07 Proceedings of the 7th international conference on Parallel processing and applied mathematics
ACM Transactions on Mathematical Software (TOMS)
A Novel Parallel QR Algorithm for Hybrid Distributed Memory HPC Systems
SIAM Journal on Scientific Computing
Performance modeling and optimal block size selection for the small-bulge multishift QR algorithm
ISPA'06 Proceedings of the 4th international conference on Parallel and Distributed Processing and Applications
On aggressive early deflation in parallel variants of the QR algorithm
PARA'10 Proceedings of the 10th international conference on Applied Parallel and Scientific Computing - Volume Part I
Optimally packed chains of bulges in multishift QR algorithms
ACM Transactions on Mathematical Software (TOMS)
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One approach to solving the nonsymmetric eigenvalue problem in parallel is to parallelize the QR algorithm. Not long ago, this was widely considered to be a hopeless task. Recent efforts have led to significant advances, although the methods proposed up to now have suffered from scalability problems. This paper discusses an approach to parallelizing the QR algorithm that greatly improves scalability. A theoretical analysis indicates that the algorithm is ultimately not scalable, but the nonscalability does not become evident until the matrix dimension is enormous. Experiments on the Intel Paragon system, the IBM SP2 supercomputer, the SGI Origin 2000, and the Intel ASCI Option Red supercomputer are reported.