DVDSON

A Davidson program for finding a few selected extreme eigenpairs of a large, sparse, real, symmetric matrix A program is presented for determining a few selected eigenvalues and their eigenvectors on either end of the spectrum of a large, real, symmetric matrix. Based on the Davidson method, which is extensively used in quantum chemistry/physics, the current implementation improves the power of the original algorithm by adopting several extensions. The matrix-vector multiplication routine that it requires is to be provided by the user. Different matrix formats and optimizations are thus feasible. Examples of an efficient sparse matrix representation and a matrix-vector multiplication are given. Some comparisons with the Lanczos method demonstrate the efficiency of the program.


References in zbMATH (referenced in 15 articles )

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  1. Xue, Fei: A block preconditioned harmonic projection method for large-scale nonlinear eigenvalue problems (2018)
  2. Wen, Zaiwen; Zhang, Yin: Accelerating convergence by augmented Rayleigh-Ritz projections for large-scale eigenpair computation (2017)
  3. Liu, Xin; Wen, Zaiwen; Zhang, Yin: An efficient Gauss-Newton algorithm for symmetric low-rank product matrix approximations (2015)
  4. Bollhöfer, Matthias; Notay, Yvan: JADAMILU: a software code for computing selected eigenvalues of large sparse symmetric matrices (2007)
  5. Dziubak, Tomasz; Matulewski, Jacek: An object-oriented C++ implementation of Davidson method for finding a few selected extreme eigenpairs of a large, sparse, real, symmetric matrix (2007)
  6. Fischer, Charlotte Froese; Tachiev, Georgio; Gaigalas, Gediminas; Godefroid, Michel R.: An MCHF atomic-structure package for large-scale calculations (2007) ioport
  7. Jönsson, P.; He, X.; Fischer, C. Froese; Grant, I. P.: The grasp2k relativistic atomic structure package (2007)
  8. Fritzsche, S.; Fischer, C. Froese; Gaigalas, G.: RELCI: A program for relativistic configuration interaction calculations (2002)
  9. Hibbert, A.: Charlotte Froese Fischer -- some personal reflections (2001)
  10. Mitin, Alexander V.: New methods for calculations of the lowest eigenvalues of the real symmetric generalized eigenvalue problem (2000)
  11. van Gisbergen, S. J. A.; Snijders, J. G.; Baerends, E. J.: Implementation of time-dependent density functional response equations (1999)
  12. Borges, Leonardo; Oliveira, Suely: A parallel Davidson-type algorithm for several eigenvalues (1998)
  13. Saad, Y.; Stathopoulos, A.; Chelikowsky, J.; Wu, K.; Öǧüt, S.: Solution of large eigenvalue problems in electronic structure calculations (1996)
  14. Stathopoulos, Andreas; Saad, Yousef; Fischer, Charlotte F.: Robust preconditioning of large, sparse, symmetric eigenvalue problems (1995)
  15. Stathopoulos, Andreas; Fischer, Charlotte F.: A Davidson program for finding a few selected extreme eigenpairs of a large, sparse, real, symmetric matrix (1994)