OpenMP Implementation of the Householder Reduction for Large Complex Hermitian Eigenvalue Problems

The computation of the complete spectrum of a complex Hermitian matrix typically proceeds through a Householder step. If only eigenvalues are needed, this Householder step needs almost the complete CPU time. Here we report our own parallel implementation of this Householder step using different variants of C and OpenMP. As far as we are aware, this is the only existing parallel implementation of the Householder reduction for complex Hermitian matrices which supports packed storage mode. As an additional feature we have implemented checkpoints which allow us to go to dimensions beyond 100 000. We perform runtime measurements and show firstly that even in serial mode the performance of our code is comparable to commercial libraries and that secondly we can obtain good parallel speedup.