Algorithm 953: parallel library software for the multishift QR algorithm with aggressive early deflation. Library software implementing a parallel small-bulge multishift QR algorithm with Aggressive Early Deflation (AED) targeting distributed memory high-performance computing systems is presented. Starting from recent developments of the parallel multishift QR algorithm [the firs author et al., SIAM J. Sci. Comput. 32, No. 4, 2345--2378 (2010; Zbl 1216.65044)], we describe a number of algorithmic and implementation improvements. These include communication avoiding algorithms via data redistribution and a refined strategy for balancing between multishift QR sweeps and AED. Guidelines concerning several important tunable algorithmic parameters are provided. As a result of these improvements, a computational bottleneck within AED has been removed in the parallel multishift QR algorithm. A performance model is established to explain the scalability behavior of the new parallel multishift QR algorithm. Numerous computational experiments confirm that our new implementation significantly outperforms previous parallel implementations of the QR algorithm.

Keywords for this software

Anything in here will be replaced on browsers that support the canvas element