An overview of dense eigenvalue solvers for distributed memory systems

Abstract

Solving large-scale eigenvalue problems presents a central problem in many research fields, such as electronic structure calculation, macromolecular simulations, solid states, theoretical physics, and combinatorial optimizations. Computing the required eigenvalues and the corresponding eigenvectors of the large matrices is a challenging task requiring significant computational time. Therefore, the computation of such problems is usually executed on large computational resources, consisting of a large number of compute nodes connected with fast interconnection links and, more often, equipped with the accelerators, such as graphic processing units. Nowadays, when the whole world races for the first exascale supercomputer and the research computational appetites are bigger than ever, the need for scalable and high-performance eigenvalue solvers, capable of exploiting such large, distributed-memory machines, is of crucial importance for the further breakthroughs in the research. This paper gives an overview of the existing numerical linear algebra packages and libraries implementing solvers for dense eigenvalue problems, tailored for distributed-memory systems. The overview analysis showed that numerous eigensolvers for distributed-memory systems exist, however, not many of them are capable of exploiting the full potential of the modern, heterogeneous, GPU-based machines with complex memory hierarchies.