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
Online Access:	Get full text
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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