Accelerating Computation of Eigenvectors in the Dense Nonsymmetric Eigenvalue Problem

In the dense nonsymmetric eigenvalue problem, work has focused on the Hessenberg reduction and QR iteration, using efficient algorithms and fast, Level 3 BLAS. 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 solution of the eigenvalue problem. To address this, we present improvements for the eigenvector computation to use Level 3 BLAS and parallelize the triangular solves, achieving good parallel scaling and accelerating the overall eigenvalue problem more than three-fold.