A Parallel Generator of Non-Hermitian Matrices Computed from Given Spectra
| Autor: | Yutong Lu, Serge G. Petiton, Xinzhe Wu |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Iterative method
Computer science MathematicsofComputing_NUMERICALANALYSIS 010103 numerical & computational mathematics 02 engineering and technology 01 natural sciences Hermitian matrix Linear algebra Convergence (routing) 0202 electrical engineering electronic engineering information engineering 020201 artificial intelligence & image processing Generator matrix 0101 mathematics Algorithm Eigenvalues and eigenvectors Sparse matrix Generator (mathematics) |
| Zdroj: | High Performance Computing for Computational Science – VECPAR 2018 ISBN: 9783030159955 VECPAR |
| Popis: | Iterative linear algebra methods are the important parts of the overall computing time of applications in various fields since decades. Recent research related to social networking, big data, machine learning and artificial intelligence has increased the necessity for non-hermitian solvers associated with much larger sparse matrices and graphs. The analysis of the iterative method behaviors for such problems is complex, and it is necessary to evaluate their convergence to solve extremely large non-Hermitian eigenvalue and linear problems on parallel and/or distributed machines. This convergence depends on the properties of spectra. Then, it is necessary to generate large matrices with known spectra to benchmark the methods. These matrices should be non-Hermitian and non-trivial, with very high dimension. This paper highlights a scalable matrix generator that uses the user-defined spectrum to construct large-scale sparse matrices and to ensure their eigenvalues as the given ones with high accuracy. This generator is implemented on CPUs and multi-GPU platforms. Good strong and weak scaling performance is obtained on several supercomputers. We also propose a method to verify its ability to guarantee the given spectra. |
| Databáze: | OpenAIRE |
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