The Eigenvalues Slicing Library (EVSL): Algorithms, implementation, and software. This paper describes a software package called EVSL (for EigenValues Slicing Library) for solving large sparse real symmetric standard and generalized eigenvalue problems. As its name indicates, the package exploits spectrum slicing, a strategy that consists of dividing the spectrum into a number of subintervals and extracting eigenpairs from each subinterval independently. In order to enable such a strategy, the methods implemented in EVSL rely on a quick calculation of the spectral density of a given matrix, or a matrix pair. What distinguishes EVSL from other currently available packages is that EVSL relies entirely on filtering techniques. Polynomial and rational filtering are both implemented and are coupled with Krylov subspace methods and the subspace iteration algorithm. On the implementation side, the package offers interfaces for various scenarios including matrix-free modes, whereby the user can supply his/her own functions to perform matrix-vector operations or to solve sparse linear systems. The paper describes the algorithms in EVSL, provides details on their implementations, and discusses performance issues for the various methods.

References in zbMATH (referenced in 11 articles , 2 standard articles )

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  1. Kalantzis, Vassilis; Xi, Yuanzhe; Horesh, Lior: Fast randomized non-Hermitian eigensolvers based on rational filtering and matrix partitioning (2021)
  2. Kollnig, Konrad; Bientinesi, Paolo; Di Napoli, Edoardo A.: Rational spectral filters with optimal convergence rate (2021)
  3. Li, Ruipeng; Sjögreen, Björn; Meier Yang, Ulrike: A new class of AMG interpolation methods based on matrix-matrix multiplications (2021)
  4. Miao, Cun-Qiang; Wu, Wen-Ting: On relaxed filtered Krylov subspace method for non-symmetric eigenvalue problems (2021)
  5. Ye, Xin; Xi, Yuanzhe; Saad, Yousef: Proxy-GMRES: preconditioning via GMRES in polynomial space (2021)
  6. Polizzi, Eric; Saad, Yousef: Computational materials science and engineering (2020)
  7. Williams-Young, David B.; Beckman, Paul G.; Yang, Chao: A shift selection strategy for parallel shift-invert spectrum slicing in symmetric self-consistent eigenvalue computation (2020)
  8. Li, Ruipeng; Xi, Yuanzhe; Erlandson, Lucas; Saad, Yousef: The eigenvalues slicing library (EVSL): algorithms, implementation, and software (2019)
  9. Paludetto Magri, Victor A.; Franceschini, Andrea; Janna, Carlo: A novel algebraic multigrid approach based on adaptive smoothing and prolongation for ill-conditioned systems (2019)
  10. Winkelmann, Jan; Springer, Paul; Di Napoli, Edoardo: ChASE: Chebyshev accelerated subspace iteration eigensolver for sequences of Hermitian eigenvalue problems (2019)
  11. Ruipeng Li, Yuanzhe Xi, Lucas Erlandson, Yousef Saad: The Eigenvalues Slicing Library (EVSL): Algorithms, Implementation, and Software (2018) arXiv