Abstract
The QZ algorithm reduces a regular matrix pair to generalized Schur form, which can be used to address the generalized eigenvalue problem. This paper summarizes recent work on improving the performance of the QZ algorithm on serial machines and work in progress on a novel parallel implementation. In both cases, the QZ iterations are based on chasing chains of tiny bulges. This allows to formulate the majority of the computation in terms of matrix-matrix multiplications, resulting in natural parallelism and better performance on modern computing systems with memory hierarchies. In addition, advanced deflation strategies are used, specifically the so called aggressive early deflation, leading to a considerable convergence acceleration and consequently to a reduction of floating point operations and computing time.
This work was supported by the DFG Emmy Noether fellowship KR 2950/1-1 and by the Swedish Research Council under grant VR 621-2001-3284 and by the Swedish Foundation for Strategic Research under grant A3 02:128. This research was conducted using the resources of the High Performance Computing Center North (HPC2N).
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Adlerborn, B., Kågström, B., Kressner, D. (2007). Parallel Variants of the Multishift QZ Algorithm with Advanced Deflation Techniques. In: Kågström, B., Elmroth, E., Dongarra, J., Waśniewski, J. (eds) Applied Parallel Computing. State of the Art in Scientific Computing. PARA 2006. Lecture Notes in Computer Science, vol 4699. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75755-9_15
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