A parallel generator of non‐Hermitian matrices computed from given spectra. (27th February 2020)

• Record Type: Journal Article
• Authors: Wu, Xinzhe; Petiton, Serge G.; Lu, Yutong
• Other Names: Gil‐Costa Veronica guestEditor.; Senger Hermes guestEditor.; Robinson Timothy W. guestEditor.; Thota Abhinav guestEditor.
• Is Part Of: Concurrency and computation. Volume 32:Number 20(2020)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2020-02-27
• Subjects: iterative methods -- linear system and eigenvalue problem -- matrix generation -- non‐Hermitian matrix -- parallel computing -- spectrum; Parallel processing (Electronic computers) -- Periodicals; Parallel computers -- Periodicals; 004.35
• DOI: 10.1002/cpe.5710
• Languages: English
• ISSNs: 1532-0626

Abstract

Summary: Iterative linear algebra methods to solve linear systems and eigenvalue problems with non‐Hermitian matrices are important for both the simulation arising from diverse scientific fields and the applications related to big data, machine learning, and artificial intelligence. The spectral property of these matrices has impacts on the convergence of these solvers. Moreover, with the increase of the size of applications, iterative methods are implemented in parallel on clusters. Analysis of their behaviors with non‐Hermitian matrices on supercomputers is so complex that we need to generate large‐scale matrices with different given spectra for benchmarking. These test matrices should be non‐Hermitian and nontrivial, with high dimension. This paper highlights a scalable matrix generator that constructs large sparse matrices using the user‐defined spectrum, and the eigenvalues of generated matrices are ensured to be the same as the predefined spectrum. This generator is implemented on CPUs and multi‐GPUs platforms, with good strong and weak scaling performance on several supercomputers. We also propose a method to verify its ability to guarantee the given spectra. Finally, we give an example to evaluate the numerical properties and parallel performance of iterative methods using this matrix generator.