The solution of real symmetric dense eigenvalue problems is one of the fundamental matrix computations. To date, several new high-performance eigensolvers have been developed for peta and postpeta scale systems. One of these, the EigenExa eigensolver, has been developed in Japan. EigenExa provides two routines: eigen_s, which is based on traditional tridiagonalization, and eigen_sx, which employs a new method via a pentadiagonal matrix. Recently, we conducted a detailed performance evaluation of EigenExa by using 4,800 nodes of the Oakleaf-FX supercomputer system. In this paper, we report the results of our evaluation, which is mainly focused on investigating the differences between the two routines.
The results clearly indicate both the advantages and disadvantages of eigen_sx over eigen_s, which will contribute to further performance improvement of EigenExa. The obtained results are also expected to be useful for other parallel dense matrix computations, in addition to eigenvalue problems. We have successfully solved a world largest-scale dense eigenvalue problem (one million dimension) by EigenExa taking advantage of the overall nodes (82,944 processors) of K computer in 3,464 seconds. Our EigenExa achieves 1.7 PFLOPS (16% of the K computer’s peak performance). It is the world highest performance for solving an eigenvalue problem of a dense matrix.