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Parallel Variants of the Multishift QZ Algorithm with Advanced Deflation Techniques
Umeå University, Faculty of Science and Technology, Department of Computing Science. Umeå University, Faculty of Science and Technology, High Performance Computing Center North (HPC2N).
Umeå University, Faculty of Science and Technology, Department of Computing Science. Umeå University, Faculty of Science and Technology, High Performance Computing Center North (HPC2N).
Umeå University, Faculty of Science and Technology, Department of Computing Science. Umeå University, Faculty of Science and Technology, High Performance Computing Center North (HPC2N).
2007 (English)In: Applied Parallel Computing - State of the Art in Scientific Computing: 8th International Workshop, PARA 2006, Springer , 2007, 117-126 p.Conference paper, Published paper (Refereed)
Abstract [en]

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.

Place, publisher, year, edition, pages
Springer , 2007. 117-126 p.
Series
Lecture Notes in Computer Science, LNCS 4699
Identifiers
URN: urn:nbn:se:umu:diva-23166OAI: oai:DiVA.org:umu-23166DiVA: diva2:220756
Available from: 2009-06-02 Created: 2009-06-02 Last updated: 2016-04-19

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