PRIMME: PReconditioned Iterative MultiMethod Eigensolver. Symmetric and Hermitian eigenvalue problems enjoy a remarkable theoretical structure that allows for efficient and stable algorithms for obtaining a few required eigenpairs. This is probably one of the reasons that enabled applications requiring the solution of symmetric eigenproblems to push their accuracy and thus computational demands to unprecedented levels. Materials science, structural engineering, and some QCD applications routinely compute eigenvalues of matrices of dimension more than a million; and often much more than that! Typically, with increasing dimension comes increased ill conditioning, and thus the use of preconditioning becomes essential.

References in zbMATH (referenced in 51 articles , 1 standard article )

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  1. Bajnok, Zoltán; Oberfrank, Robin: Periodically driven perturbed CFTs: the sine-Gordon model (2022)
  2. Rontsis, Nikitas; Goulart, Paul; Nakatsukasa, Yuji: Efficient semidefinite programming with approximate ADMM (2022)
  3. Baglama, James; Bella, Tom; Picucci, Jennifer: Hybrid iterative refined method for computing a few extreme eigenpairs of a symmetric matrix (2021)
  4. Baglama, James; Bella, Tom; Picucci, Jennifer: Hybrid iterative refined method for computing a few extreme eigenpairs of a symmetric matrix (2021)
  5. Bergner, Georg; Schaich, David: Eigenvalue spectrum and scaling dimension of lattice (\mathcalN= 4) supersymmetric Yang-Mills (2021)
  6. Konik, Robert; Lájer, Márton; Mussardo, Giuseppe: Approaching the self-dual point of the sinh-Gordon model (2021)
  7. Dax, Achiya: A cross-product approach for low-rank approximations of large matrices (2020)
  8. Kalantzis, Vassilis: A spectral Newton-Schur algorithm for the solution of symmetric generalized eigenvalue problems (2020)
  9. Kalantzis, Vassilis: A domain decomposition Rayleigh-Ritz algorithm for symmetric generalized eigenvalue problems (2020)
  10. Lu, Ding: Nonlinear eigenvector methods for convex minimization over the numerical range (2020)
  11. Nakatsukasa, Yuji: Sharp error bounds for Ritz vectors and approximate singular vectors (2020)
  12. Romero, Eloy; Stathopoulos, Andreas; Orginos, Kostas: Multigrid deflation for lattice QCD (2020)
  13. Thies, Jonas; Röhrig-Zöllner, Melven; Overmars, Nigel; Basermann, Achim; Ernst, Dominik; Hager, Georg; Wellein, Gerhard: PHIST: a pipelined, hybrid-parallel iterative solver toolkit (2020)
  14. Avron, Haim; Druinsky, Alex; Toledo, Sivan: Spectral condition-number estimation of large sparse matrices. (2019)
  15. Dax, Achiya: Computing the smallest singular triplets of a large matrix (2019)
  16. Goldenberg, Steven; Stathopoulos, Andreas; Romero, Eloy: A Golub-Kahan Davidson method for accurately computing a few singular triplets of large sparse matrices (2019)
  17. Huang, Jinzhi; Jia, Zhongxiao: On inner iterations of Jacobi-Davidson type methods for large SVD computations (2019)
  18. Ju, S. H.; Hsu, H. H.: An out-of-core eigen-solver with OpenMP parallel scheme for large spare damped system (2019)
  19. Li, Ruipeng; Xi, Yuanzhe; Erlandson, Lucas; Saad, Yousef: The eigenvalues slicing library (EVSL): algorithms, implementation, and software (2019)
  20. Mor-Yosef, Liron; Avron, Haim: Sketching for principal component regression (2019)

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