From this page you can get a Matlab® implementation of the JDQR algorithm. The JDQR algorithm can be used for computing a few selected eigenvalues with some desirable property together with the associated eigenvectors of a matrix A. The matrix can be real or complex, Hermitian or non-Hermitian, .... The algorithm is effective especially in case A is sparse and of large size. The Jacobi-Davidson method is used to compute a partial Schur decomposition of A. The decomposition leads to the wanted eigenpairs.

References in zbMATH (referenced in 489 articles )

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  1. Arbenz, Peter: Towards an efficient implementation of the eigenstate expansion method for quantum molecular dynamics simulations (2000)
  2. Bai, Zhaojun (ed.); Demmel, James (ed.); Dongarra, Jack (ed.); Ruhe, Axel (ed.); Van der Vorst, Henk (ed.): Templates for the solution of algebraic eigenvalue problems. A practical guide (2000)
  3. Golub, Gene H.; van der Vorst, Henk A.: Eigenvalue computation in the 20th century (2000)
  4. Kågström, Bo; Wiberg, Petter: Extracting partial canonical structure for large scale eigenvalue problems (2000)
  5. Morgan, Ronald B.: Preconditioning eigenvalues and some comparison of solvers (2000)
  6. Ruhe, A.: The rational Krylov algorithm for nonlinear matrix eigenvalue problems (2000)
  7. Sameh, Ahmed; Tong, Zhanye: The trace minimization method for the symmetric generalized eigenvalue problem (2000)
  8. van der Veen, Hilda; Vuik, Kees; de Borst, René: Branch switching techniques for bifurcation in soil deformation (2000)
  9. Vasseur, Xavier: Analysis of a non-standard multigrid preconditioner by spectral portrait computation (2000)
  10. Wu, Kesheng; Simon, Horst: Thick-restart Lanczos method for large symmetric eigenvalue problems (2000)
  11. Arbenz, Peter; Geus, Roman: Two-level hierarchical basis preconditioners for computing eigenfrequencies of cavity resonators with the finite element method (1999)
  12. De Samblanx, Gorik; Bultheel, Adhemar: Using implicitly filtered RKS for generalised eigenvalue problems (1999)
  13. Engelborghs, Koen; Roose, Dirk: Numerical computation of stability and detection of Hopf bifurcations of steady state solutions of delay differential equations (1999)
  14. Fokkema, Diederik R.; Sleijpen, Gerard L. G.; van der Vorst, Henk A.: Jacobi-Davidson style QR and QZ algorithms for the reduction of matrix pencils (1999)
  15. Genseberger, Menno; Sleijpen, Gerard L. G.: Alternative correction equations in the Jacobi-Davidson method (1999)
  16. Arbenz, Peter; Geus, Roman: Parallel solvers for large eigenvalue problems originating from Maxwell’s equations (1998)
  17. Dongarra, Jack J.; Duff, Iain S.; Sorensen, Danny C.; Van der Vorst, Henk A.: Numerical linear algebra for high-performance computers (1998)
  18. Heeg, Ruerd S.; Geurts, Bernard J.: Spatial instabilities of the incompressible attachment-line flow using sparse matrix Jacobi-Davidson techniques (1998)
  19. Lehoucq, R. B.; Meerbergen, Karl: Using generalized Cayley transformations within an inexact rational Krylov sequence method (1998)
  20. O’Leary, D. P.; Stewart, G. W.: On the convergence of a new Rayleigh quotient method with applications to large eigenproblems (1998)

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