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 19 articles , 1 standard article )

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  1. Gambhir, Arjun Singh; Stathopoulos, Andreas; Orginos, Kostas: Deflation as a method of variance reduction for estimating the trace of a matrix inverse (2017)
  2. Scott, Tony C.; Therani, Madhusudan; Wang, Xing M.: Data clustering with quantum mechanics (2017)
  3. Kestyn, James; Polizzi, Eric; Tang, Ping Tak Peter: Feast eigensolver for non-Hermitian problems (2016)
  4. Liang, Qiao; Ye, Qiang: Deflation by restriction for the inverse-free preconditioned Krylov subspace method (2016)
  5. Li, Ruipeng; Xi, Yuanzhe; Vecharynski, Eugene; Yang, Chao; Saad, Yousef: A thick-restart Lanczos algorithm with polynomial filtering for Hermitian eigenvalue problems (2016)
  6. Xi, Yuanzhe; Saad, Yousef: Computing partial spectra with least-squares rational filters (2016)
  7. Zhou, Yunkai; Wang, Zheng; Zhou, Aihui: Accelerating large partial EVD/SVD calculations by filtered block Davidson methods (2016)
  8. 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)
  9. Schaich, David; DeGrand, Thomas: Parallel software for lattice $\mathcalN = 4$ supersymmetric Yang-Mills theory (2015)
  10. Wu, Lingfei; Stathopoulos, Andreas: A preconditioned hybrid SVD method for accurately computing singular triplets of large matrices (2015)
  11. Andrzejewski, Janusz: On optimizing Jacobi-Davidson method for calculating eigenvalues in low dimensional structures using eight band $\boldk\cdot\boldp$ model (2013)
  12. Klinvex, A.; Saied, F.; Sameh, A.: Parallel implementations of the trace minimization scheme tracemin for the sparse symmetric eigenvalue problem (2013)
  13. De Sterck, Hans: A self-learning algebraic multigrid method for extremal singular triplets and eigenpairs (2012)
  14. Romero, Eloy; Cruz, Manuel B.; Roman, Jose E.; Vasconcelos, Paulo B.: A parallel implementation of the Jacobi-Davidson eigensolver for unsymmetric matrices (2011)
  15. Stathopoulos, Andreas; McCombs, James R.: PRIMME: preconditioned iterative multimethod eigensolver -- methods and software description (2010)
  16. Baker, C.G.; Hetmaniuk, U.L.; Lehoucq, R.B.; Thornquist, H.K.: Anasazi software for the numerical solution of large-scale eigenvalue problems (2009)
  17. Vömel, Christof; Tomov, Stanimire Z.; Marques, Osni A.; Canning, A.; Wang, Lin-Wang; Dongarra, Jack J.: State-of-the-art eigensolvers for electronic structure calculations of large scale nano-systems (2008)
  18. Bollhöfer, Matthias; Notay, Yvan: JADAMILU: a software code for computing selected eigenvalues of large sparse symmetric matrices (2007)
  19. Knyazev, A.V.; Argentati, M.E.; Lashuk, I.; Ovtchinnikov, E.E.: Block locally optimal preconditioned eigenvalue xolvers (BLOPEX) in hypre and PETSC (2007)