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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.


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


Björn Adlerborn, Bo Kågström, and Daniel Kressner

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Entry responsible: Bo Kagstrom

Page Responsible: Frank Drewes