TY - EJOUR
DO - 10.1137/140954817
AB - 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.
T1 - A Parallel QZ Algorithm For Distributed Memory HPC Systems
IS - 5
DA - 2014
AU - Adlerborn, Bjoern
AU - Kagstroem, Bo
AU - Kressner, Daniel
JF - SIAM Journal On Scientific Computing
SP - C480-C503
VL - 36
EP - C480-C503
PB - Siam Publications
PP - Philadelphia
ID - 205266
KW - generalized eigenvalue problem
KW - nonsymmetric QZ algorithm
KW - multishift
KW - bulge chasing
KW - infinite eigenvalues
KW - parallel algorithms
KW - level 3 performance
KW - aggressive early deflation
ER -