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. © Springer-Verlag Berlin Heidelberg 2007.
CITATION STYLE
Adlerborn, B., Kågström, B., & Kressner, D. (2007). Parallel variants of the multishift QZ algorithm with advanced deflation techniques. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 4699 LNCS, pp. 117–126). Springer Verlag. https://doi.org/10.1007/978-3-540-75755-9_15
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