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 27 articles , 1 standard article )

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  1. Kalantzis, Vassilis; Xi, Yuanzhe; Saad, Yousef: Beyond automated multilevel substructuring: domain decomposition with rational filtering (2018)
  2. Xue, Fei: A block preconditioned harmonic projection method for large-scale nonlinear eigenvalue problems (2018)
  3. Gambhir, Arjun Singh; Stathopoulos, Andreas; Orginos, Kostas: Deflation as a method of variance reduction for estimating the trace of a matrix inverse (2017)
  4. Goldfarb, Donald; Mu, Cun; Wright, John; Zhou, Chaoxu: Using negative curvature in solving nonlinear programs (2017)
  5. Scott, Tony C.; Therani, Madhusudan; Wang, Xing M.: Data clustering with quantum mechanics (2017)
  6. Wu, Lingfei; Romero, Eloy; Stathopoulos, Andreas: PRIMME_SVDS: a high-performance preconditioned SVD solver for accurate large-scale computations (2017)
  7. Kestyn, James; Polizzi, Eric; Tang, Ping Tak Peter: Feast eigensolver for non-Hermitian problems (2016)
  8. Liang, Qiao; Ye, Qiang: Deflation by restriction for the inverse-free preconditioned Krylov subspace method (2016)
  9. Li, Ruipeng; Xi, Yuanzhe; Vecharynski, Eugene; Yang, Chao; Saad, Yousef: A thick-restart Lanczos algorithm with polynomial filtering for Hermitian eigenvalue problems (2016)
  10. Wen, Zaiwen; Yang, Chao; Liu, Xin; Zhang, Yin: Trace-penalty minimization for large-scale eigenspace computation (2016)
  11. Wu, Lingfei; Laeuchli, Jesse; Kalantzis, Vassilis; Stathopoulos, Andreas; Gallopoulos, Efstratios: Estimating the trace of the matrix inverse by interpolating from the diagonal of an approximate inverse (2016)
  12. Xi, Yuanzhe; Saad, Yousef: Computing partial spectra with least-squares rational filters (2016)
  13. Zhou, Yunkai; Wang, Zheng; Zhou, Aihui: Accelerating large partial EVD/SVD calculations by filtered block Davidson methods (2016)
  14. Röhrig-Zöllner, Melven; Thies, Jonas; Kreutzer, Moritz; Alvermann, Andreas; Pieper, Andreas; Basermann, Achim; Hager, Georg; Wellein, Gerhard; Fehske, Holger: Increasing the performance of the Jacobi-Davidson method by blocking (2015)
  15. Schaich, David; DeGrand, Thomas: Parallel software for lattice $\mathcalN = 4$ supersymmetric Yang-Mills theory (2015)
  16. Wu, Lingfei; Stathopoulos, Andreas: A preconditioned hybrid SVD method for accurately computing singular triplets of large matrices (2015)
  17. Abdel-Rehim, A. M.; Stathopoulos, Andreas; Orginos, Kostas: Extending the eigCG algorithm to nonsymmetric Lanczos for linear systems with multiple right-hand sides. (2014)
  18. Romero, Eloy; Roman, Jose E.: A parallel implementation of Davidson methods for large-scale eigenvalue problems in SLEPc (2014)
  19. Andrzejewski, Janusz: On optimizing Jacobi-Davidson method for calculating eigenvalues in low dimensional structures using eight band $\boldk\cdot\boldp$ model (2013)
  20. Klinvex, A.; Saied, F.; Sameh, A.: Parallel implementations of the trace minimization scheme tracemin for the sparse symmetric eigenvalue problem (2013)

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