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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| Published in: | SC24-W: Workshops of the International Conference for High Performance Computing, Networking, Storage and Analysis pp. 1703 - 1712 |
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| Main Authors: | , |
| Format: | Conference Proceeding |
| Language: | English |
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IEEE
17.11.2024
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| Abstract | 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. |
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| AbstractList | 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. |
| Author | Uchino, Yuki Imamura, Toshiyuki |
| Author_xml | – sequence: 1 givenname: Yuki surname: Uchino fullname: Uchino, Yuki email: yuki.uchino.fe@riken.jp organization: RIKEN Center for Computational Science,Kobe, Hyogo,Japan – sequence: 2 givenname: Toshiyuki surname: Imamura fullname: Imamura, Toshiyuki email: imamura.toshiyuki@riken.jp organization: RIKEN Center for Computational Science,Kobe, Hyogo,Japan |
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| Snippet | This study proposes a high-performance and reliable eigensolver via mixed-precision arithmetic between ordinary and highly-accurate precisions. Eigenvalue... |
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| StartPage | 1703 |
| SubjectTerms | Accuracy accurate numerical computation Approximation algorithms Conferences eigenvalue decomposition Eigenvalues and eigenfunctions Error analysis High performance computing Iterative algorithms iterative refinement Reliability Scalability Supercomputers |
| Title | High-Performance Eigensolver Combining EigenExa and Iterative Refinement |
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