High-Performance Eigensolver Combining EigenExa and Iterative Refinement

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 na...

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Bibliographic Details
Published in:SC24-W: Workshops of the International Conference for High Performance Computing, Networking, Storage and Analysis pp. 1703 - 1712
Main Authors: Uchino, Yuki, Imamura, Toshiyuki
Format: Conference Proceeding
Language:English
Published: IEEE 17.11.2024
Subjects:
Accuracy
accurate numerical computation
Approximation algorithms
Conferences
eigenvalue decomposition
Eigenvalues and eigenfunctions
Error analysis
High performance computing
Iterative algorithms
iterative refinement
Reliability
Scalability
Supercomputers
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Summary: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.
DOI:10.1109/SCW63240.2024.00213