An improved mixed-precision FEAST algorithm for solving symmetric eigenvalue problems
Solving symmetric eigenvalue problems is vital in many areas of scientific computing. FEAST is a well-known package designed for large-scale eigenvalue problems, incorporating mixed-precision techniques to accelerate linear equation solving. Unlike FEAST's approach, this work introduces a new m...
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| Vydáno v: | 2024 IEEE International Conference on High Performance Computing and Communications (HPCC) s. 721 - 728 |
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13.12.2024
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| Abstract | Solving symmetric eigenvalue problems is vital in many areas of scientific computing. FEAST is a well-known package designed for large-scale eigenvalue problems, incorporating mixed-precision techniques to accelerate linear equation solving. Unlike FEAST's approach, this work introduces a new mixed-precision method that approximates the original eigenvalue problem at a lower precision to quickly provide a good initial guess. These results are then used to accelerate the convergence in working precision. Extensive experiments on large sparse matrices from real applications and randomly generated banded matrices demonstrate the effectiveness of this approach. In appropriate circumstances, our improved mixed-precision FEAST algorithm achieves an average speedup of 1.58× compared to the double-precision FEAST algorithm, with a maximum speedup of 1.79×. Additionally, compared to the original mixed-precision approach in the latest FEAST library, our method offers up to a 1.43× performance improvement. |
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| AbstractList | Solving symmetric eigenvalue problems is vital in many areas of scientific computing. FEAST is a well-known package designed for large-scale eigenvalue problems, incorporating mixed-precision techniques to accelerate linear equation solving. Unlike FEAST's approach, this work introduces a new mixed-precision method that approximates the original eigenvalue problem at a lower precision to quickly provide a good initial guess. These results are then used to accelerate the convergence in working precision. Extensive experiments on large sparse matrices from real applications and randomly generated banded matrices demonstrate the effectiveness of this approach. In appropriate circumstances, our improved mixed-precision FEAST algorithm achieves an average speedup of 1.58× compared to the double-precision FEAST algorithm, with a maximum speedup of 1.79×. Additionally, compared to the original mixed-precision approach in the latest FEAST library, our method offers up to a 1.43× performance improvement. |
| Author | Li, Shengguo Li, Tiejun Xie, Yi Shao, Meiyue Ren, Ruixuan |
| Author_xml | – sequence: 1 givenname: Yi surname: Xie fullname: Xie, Yi email: xieyi00@nudt.edu.cn organization: College of Computer Science and Technology National University of Defense Technology,Changsha,China – sequence: 2 givenname: Shengguo surname: Li fullname: Li, Shengguo email: nudtlsg@nudt.edu.cn organization: College of Computer Science and Technology National University of Defense Technology,Changsha,China – sequence: 3 givenname: Tiejun surname: Li fullname: Li, Tiejun email: tjli@nudt.edu.cn organization: College of Computer Science and Technology National University of Defense Technology,Changsha,China – sequence: 4 givenname: Meiyue surname: Shao fullname: Shao, Meiyue email: myshao@fudan.edu.cn organization: School of Data Science and MOE Key Laboratory for Computational Physical Sciences Fudan University,Shanghai,China – sequence: 5 givenname: Ruixuan surname: Ren fullname: Ren, Ruixuan email: renruixuan18@nudt.edu.cn organization: College of Computer Science and Technology National University of Defense Technology,Changsha,China |
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| Snippet | Solving symmetric eigenvalue problems is vital in many areas of scientific computing. FEAST is a well-known package designed for large-scale eigenvalue... |
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| SubjectTerms | Banded Matrix Convergence Eigenvalues and eigenfunctions FEAST High performance computing Iterative methods Libraries Linear systems Mixed-Precision Algorithm Performance gain Scientific computing Sparse matrices Symmetric Eigenvalue Problem Symmetric matrices |
| Title | An improved mixed-precision FEAST algorithm for solving symmetric eigenvalue problems |
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