Performance of the block Jacobi method for the symmetric eigenvalue problem on a modern massively parallel computer

Abstract

In this paper, we consider the solution of a medium-size symmetric eigenvalue problem on a massively parallel computer using the block Jacobi method. We compare parallel cyclic block Jacobi methods using 1-dimensional and 2-dimensional data distribution and show that the latter has advantages in terms of the number of processors that can be used and the frequency and volume of interprocessor communication. The 2-dimensional scheme has a disadvantage that some part of the algorithm can be executed by only pp processors, where p is the number of processors. However, a simple analysis shows that this does not degrade weak scalability. This analysis is supported by performance evaluation on the University of Tokyo’s T2K supercomputer using up to 1024 cores. We also discuss how to improve the performance of our imlementation from three viewpoints.