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UMINF 14.03

A Parallel QZ Algorithm for Distributed Memory HPC Systems

Appearing frequently in applications, generalized eigenvalue problems represent one of the core problems in numerical linear algebra. The QZ algorithm by Moler and Stewart is the most widely used algorithm for addressing such problems. Despite its importance, little attention has been paid to the parallelization of the QZ algorithm. The purpose of this work is to fill this gap. We propose a parallelization of the QZ algorithm that incorporates all modern ingredients of dense eigensolvers, such as multishift and aggressive early deflation techniques. To deal with (possibly many) infi nite eigenvalues, a new parallel deflation strategy is developed. Numerical experiments for several random and application examples demonstrate the e ectiveness of our algorithm on two diff erent distributed memory HPC systems.

Keywords

Generalized eigenvalue problem, nonsymmetric QZ algorithm, multishifts, bulge chasing, infinite eigenvalues, parallel algorithms, level 3 performance, aggressive early deflation.

Authors

Björn Adlerborn, Bo Kågström, and Daniel Kressner

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Entry responsible: Bo Kagstrom

Page Responsible: Frank Drewes
2024-06-17