Adlerborn, Bjoern
Kagstroem, Bo
Kressner, Daniel
A Parallel QZ Algorithm For Distributed Memory HPC Systems
SIAM Journal On Scientific Computing
10.1137/140954817
36
5
C480-C503
24
Appearing frequently in applications, generalized eigenvalue problems represent one of the core problems in numerical linear algebra. The QZ algorithm of 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) infinite eigenvalues, a new parallel deflation strategy is developed. Numerical experiments for several random and application examples demonstrate the effectiveness of our algorithm on two different distributed memory HPC systems.
generalized eigenvalue problem;
nonsymmetric QZ algorithm;
multishift;
bulge chasing;
infinite eigenvalues;
parallel algorithms;
level 3 performance;
aggressive early deflation;
Siam Publications
Philadelphia
2014