Accelerating Computation of Eigenvectors in the Dense Nonsymmetric Eigenvalue Problem

Abstract. In the dense nonsymmetric eigenvalue problem, work has focused on the Hessenberg reduction and QR iteration, using efficient al-gorithms and fast, Level 3 BLAS. Comparatively, computation of eigen-vectors 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 im-provements for the eigenvector computation to use Level 3 BLAS and parallelize the triangular solves, achieving good parallel scaling and ac-celerating the overall eigenvalue problem more than three-fold.