High-Performance Eigensolver Combining EigenExa and Iterative Refinement - Uchino, Yuki; Imamura, Toshiyuki (SC24-W: Workshops of the International Conference for High Performance Computing, Networking, Storage and Analysis, 2024)
This study proposes a high-performance and reliable eigensolver via mixed-precision arithmetic between ordinary and highly-accurate precisions. Eigenvalue decomposition is ubiquitous in simulations. Various eigensolvers for computing approximations have been developed thus far. If eigenvalues are narrowly clustered, the computation of eigenvectors may be ill-posed. Thus, the computed eigenpairs may not be sufficiently accurate and lack reliability. In this study, we introduce mixed-precision iterative refinement methods to improve the accuracy of eigenvectors obtained using numerical methods. This approach contributes to obtaining sufficiently accurate results without arbitrary precision eigensolvers. We construct a high-performance and reliable eigensolver by combining the iterative refinement methods and EigenExa, a modern high-performance solver for large-scale and highly parallel computations. Numerical experiment results demonstrate the accuracy of the results and performance benchmark of the proposed approach.