Published March 3, 2014 as ut-eecs-14-726
In the nonsymmetric eigenvalue problem, work has focused on the Hessenberg reduction and QR iteration, using efficient algorithms and fast, Level 3 BLAS routines. Comparatively, computation of eigenvectors performs poorly, limited to slow, Level 2 BLAS performance with little speedup on multi-core systems. It has thus become a dominant cost in the eigenvalue problem. To address this, we present improvements for the eigenvector computation to use Level 3 BLAS where applicable and parallelize the remaining triangular solves, achieving good parallel scaling and accelerating the overall eigenvalue problem more than three-fold.
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