Block Locally Optimal Preconditioned Eigenvalue Xolvers (BLOPEX) is a package, written in C and MATLAB/OCTAVE, that includes an eigensolver implemented with the Locally Optimal Block Preconditioned Conjugate Gradient Method (LOBPCG). Its main features are: a matrix-free iterative method for computing several extreme eigenpairs of symmetric positive generalized eigenproblems; a user-defined symmetric positive preconditioner; robustness with respect to random initial approximations, variable preconditioners, and ill-conditioning of the stiffness matrix; and apparently optimal convergence speed. BLOPEX supports parallel MPI-based computations. BLOPEX is incorporated in the HYPRE package and is available as an external block to the PETSc package. SLEPc and PHAML have interfaces to call BLOPEX eigensolvers, as well as DevTools by Visual Kinematics.

References in zbMATH (referenced in 27 articles , 1 standard article )

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  1. Xu, Fei; Xie, Hehu; Zhang, Ning: A parallel augmented subspace method for eigenvalue problems (2020)
  2. Li, Ruipeng; Xi, Yuanzhe; Erlandson, Lucas; Saad, Yousef: The eigenvalues slicing library (EVSL): algorithms, implementation, and software (2019)
  3. Pandur, Marija Miloloža: Preconditioned gradient iterations for the eigenproblem of definite matrix pairs (2019)
  4. Rakhuba, Maxim; Novikov, Alexander; Oseledets, Ivan: Low-rank Riemannian eigensolver for high-dimensional Hamiltonians (2019)
  5. Shen, Yedan; Kuang, Yang; Hu, Guanghui: An asymptotics-based adaptive finite element method for Kohn-Sham equation (2019)
  6. Wu, Lingfei; Xue, Fei; Stathopoulos, Andreas: TRPL+K: thick-restart preconditioned Lanczos+K method for large symmetric eigenvalue problems (2019)
  7. Duersch, Jed A.; Shao, Meiyue; Yang, Chao; Gu, Ming: A robust and efficient implementation of LOBPCG (2018)
  8. Teng, Zhongming; Wang, Xuansheng: Heavy ball restarted CMRH methods for linear systems (2018)
  9. Cai, Zhiqiang; Cao, Shuhao; Falgout, Rob: Robust a posteriori error estimation for finite element approximation to (\boldsymbolH(\mathbfcurl)) problem (2016)
  10. Kestyn, James; Polizzi, Eric; Tang, Ping Tak Peter: Feast eigensolver for non-Hermitian problems (2016)
  11. Vecharynski, Eugene; Yang, Chao; Xue, Fei: Generalized preconditioned locally harmonic residual method for non-Hermitian eigenproblems (2016)
  12. Wen, Zaiwen; Yang, Chao; Liu, Xin; Zhang, Yin: Trace-penalty minimization for large-scale eigenspace computation (2016)
  13. Banerjee, Amartya S.; Elliott, Ryan S.; James, Richard D.: A spectral scheme for Kohn-Sham density functional theory of clusters (2015)
  14. Vecharynski, Eugene; Knyazev, Andrew: Preconditioned locally harmonic residual method for computing interior eigenpairs of certain classes of Hermitian matrices (2015)
  15. Vecharynski, Eugene; Yang, Chao; Pask, John E.: A projected preconditioned conjugate gradient algorithm for computing many extreme eigenpairs of a Hermitian matrix (2015)
  16. Romero, Eloy; Roman, Jose E.: A parallel implementation of Davidson methods for large-scale eigenvalue problems in SLEPc (2014)
  17. Bao, Gang; Hu, Guanghui; Liu, Di: Numerical solution of the Kohn-Sham equation by finite element methods with an adaptive mesh redistribution technique (2013)
  18. Lin, Lin; Shao, Sihong; E, Weinan: Efficient iterative method for solving the Dirac-Kohn-Sham density functional theory (2013)
  19. Bao, Gang; Hu, Guanghui; Liu, Di: An (h)-adaptive finite element solver for the calculations of the electronic structures (2012)
  20. Demmel, James; Grigori, Laura; Hoemmen, Mark; Langou, Julien: Communication-optimal parallel and sequential QR and LU factorizations (2012)

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