engleski

An overview of dense eigenvalue solvers for distributed memory systems

Solving large-scale eigenvalue problems is a central problem in many research areas, such as electronic structure calculations, macromolecular simulations, solid states, theoretical physics, and combinatorial optimization. The computation of the required eigenvalues and the corresponding eigenvectors of the large matrices is a challenging task that requires considerable computational time. Therefore, the computation of such problems is usually performed on large computational resources consisting of a large number of computational nodes interconnected by fast network and often equipped with accelerators, such as graphic processing units. Nowadays, when the whole world is vying for the first exascale supercomputer and the computational appetite of researchers is greater than ever, the need for scalable and powerful eigenvalue solvers capable of utilising such large machines with distributed memory is crucial for further breakthroughs in research. This paper reviews existing numerical linear algebra packages and libraries that implement solvers for dense eigenvalue problems and are tailored to distributed-memory systems. The survey analysis has shown that there are numerous eigenvalue solvers for distributed memory systems. However, not many of them are able to exploit the full potential of modern, heterogeneous, GPU- based machines with complex memory hierarchies.

eigenvalue solvers ; high-performance computing ; distributed-memory ; large-scale systems

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