Multi-GPU Scalable Implementation of a Contour-Integral-Based Eigensolver for Real Symmetric Dense Generalized Eigenvalue Problems

We consider a parallel eigensolver for generalized eigenvalue problems for distributed GPU systems. In this paper, we propose a distributed parallel implementation of the Sakurai-Sugiura (SS) eigenvalue solver for solving generalized eigenvalue problems with real symmetric matrices using GPU linear algebra libraries. In the SS method, the target subspace is constructed from solutions of linear systems. The dominant part of this method is calculating solutions of linear equations. By assigning the solution of independent linear systems to each GPU, a coarse-grained parallelism can be obtained, and high scalability is expected. We also proposed the performance model of this implementation. We evaluate its parallel performance using numerical examples that involve medium-size dense matrices.