Parallel variants of the multishift QZ algorithm with advanced deflation techniques

Authors:
Björn Adlerborn;Bo Kågström;Daniel Kressner
Affiliations:
Department of Computing Science, Umeå University, Umeå, Sweden;Department of Computing Science, Umeå University, Umeå, Sweden;Department of Computing Science, Umeå University, Umeå, Sweden
Venue:
PARA'06 Proceedings of the 8th international conference on Applied parallel computing: state of the art in scientific computing
Year:
2006

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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.