  We present a high-performance solver for dense skew-symmetric matrix
eigenvalue problems. Our work is motivated by applications in computational
quantum physics, where one solution approach to solve the so-called
Bethe-Salpeter equation involves the solution of a large, dense, skew-symmetric
eigenvalue problem. The computed eigenpairs can be used to compute the optical
absorption spectrum of molecules and crystalline systems. One state-of-the art
high-performance solver package for symmetric matrices is the ELPA (Eigenvalue
SoLvers for Petascale Applications) library. We extend the methods available in
ELPA to skew-symmetric matrices. This way, the presented solution method can
benefit from the optimizations available in ELPA that make it a
well-established, efficient and scalable library, such as GPU support. We
compare performance and scalability of our method to the only available
high-performance approach for skew-symmetric matrices, an indirect route
involving complex arithmetic. In total, we achieve a performance that is up to
3.67 higher than the reference method using Intel's ScaLAPACK implementation.
The runtime to solve the Bethe-Salpeter-Eigenvalue problem can be improved by a
factor of 10. Our method is freely available in the current release of the ELPA
library.
