Matlab® implementation of the JDQZ algorithm. The JDQZ algorithm can be used for computing a few selected eigenvalues with some desirable property together with the associated eigenvectors of a matrix pencil A-lambda*B. The matrices can be real or complex, Hermitian or non-Hermitian, .... The algorithm is effective especially in case A and B are sparse and of large size. The Jacobi-Davidson method is used to compute a partial generalized Schur decomposition of the pair (A,B). The decomposition leads to the wanted eigenpairs.

References in zbMATH (referenced in 557 articles , 1 standard article )

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  1. Sleijpen, Gerard L. G.; Van der Vorst, Henk A.: A Jacobi-Davidson iteration method for linear eigenvalue problems (1998)
  2. Sorensen, D. C.: Truncated (QZ) methods for large scale generalized eigenvalue problems (1998)
  3. Sorensen, D. C.; Yang, C.: A truncated RQ iteration for large scale eigenvalue calculations (1998)
  4. Stathopoulos, Andreas; Saad, Yousef; Wu, Kesheng: Dynamic thick restarting of the Davidson, and the implicitly restarted Arnoldi methods (1998)
  5. Wu, Kesheng; Saad, Yousef; Stathopoulos, Andreas: Inexact Newton preconditioning techniques for large symmetric eigenvalue problems (1998)
  6. Zhang, T.; Golub, G. H.; Law, K. H.: Eigenvalue perturbation and generalized Krylov subspace method (1998)
  7. de Samblanx, G.; Meerbergen, K.; Bultheel, A.: The implicit application of a rational filter in the RKS method (1997)
  8. Lai, Y.; Lin, K.; Lin, W.: An inexact inverse iteration for large sparse eigenvalue problems (1997)
  9. Meerbergen, Karl; Roose, Dirk: The restarted Arnoldi method applied to iterative linear system solvers for the computation of rightmost eigenvalues (1997)
  10. van der Vorst, Henk A.; Golub, Gene H.: 150 years old and still alive: Eigenproblems (1997)
  11. van Dorsselaer, Jos L. M.: Computing eigenvalues occurring in continuation methods with the Jacobi-Davidson QZ method (1997)
  12. van Dorsselaer, Jos L. M.: Pseudospectra for matrix pencils and stability of equilibria (1997)
  13. Fattebert, Jean-Luc: An inverse iteration method using multigrid for quantum chemistry (1996)
  14. Simoncini, V.: Ritz and pseudo-Ritz values using matrix polynomials (1996)
  15. Sleijpen, Gerard L. G.; Booten, Albert G. L.; Fokkema, Diederik R.; Van der Vorst, Henk A.: Jacobi-Davidson type methods for generalized eigenproblems and polynomial eigenproblems (1996)
  16. Sleijpen, Gerard L. G.; van der Vorst, Henk A.: A Jacobi-Davidson iteration method for linear eigenvalue problems (1996)
  17. Toh, Kim-Chuan; Trefethen, Lloyd N.: Calculation of pseudospectra by the Arnoldi iteration (1996)

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