Optimization research on solving tridiagonal matrix eigenproblems based on divide and conquer on GPU-like accelerators

Bo Liu; JianPeng Sun; HongPeng Zhao; WuDi Cao; QingWei Wang

doi:10.1117/12.2685638

21 July 2023 Optimization research on solving tridiagonal matrix eigenproblems based on divide and conquer on GPU-like accelerators

Bo Liu, JianPeng Sun, HongPeng Zhao, WuDi Cao, QingWei Wang

Author Affiliations +

Proceedings Volume 12717, 3rd International Conference on Artificial Intelligence, Automation, and High-Performance Computing (AIAHPC 2023); 127170E (2023) https://doi.org/10.1117/12.2685638
Event: 3rd International Conference on Artificial Intelligence, Automation, and High-Performance Computing (AIAHPC 2023), 2023, Wuhan, China

Abstract

In scientific and engineering computations, it is often necessary to solve eigenvalue problems of symmetric matrices. With the rapid development of high-performance computing, the adaptation and optimization of linear algebra solution methods, including eigenvalue problem solving, on heterogeneous platforms have become increasingly important. In this paper, we propose a divide-and-conquer method for solving symmetric matrix eigenvalue problems, which is implemented based on the SOLVER library of domestic heterogeneous platforms using the HIP programming model. We take full advantage of the multicore strengths of domestic accelerators and parallelize the solution process, such as the secular equation. Parallel reduction and merged computation optimization techniques are employed to further improve performance. Compared with implementations such as MAGMA, our optimized interface demonstrates good stability and high accuracy in various scale test cases of real-world applications, as well as a significant performance advantage. The results show that in large-scale matrix eigenvalue problems, the performance is more than twice that of the related interfaces in the MAGMA library.

Citation Download Citation

Bo Liu, JianPeng Sun, HongPeng Zhao, WuDi Cao, and QingWei Wang "Optimization research on solving tridiagonal matrix eigenproblems based on divide and conquer on GPU-like accelerators", Proc. SPIE 12717, 3rd International Conference on Artificial Intelligence, Automation, and High-Performance Computing (AIAHPC 2023), 127170E (21 July 2023); https://doi.org/10.1117/12.2685638

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KEYWORDS

Matrices

Interfaces

Mathematical optimization

Eigenvectors

Linear algebra

Parallel computing

Chemical elements

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