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 589 articles , 1 standard article )

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  1. Meerbergen, Karl: Locking and restarting quadratic eigenvalue solvers (2001)
  2. Mehrmann, Volker; Watkins, David: Structure-preserving methods for computing eigenpairs of large sparse skew-Hamiltonian/Hamiltonian pencils (2001)
  3. Ovtchinnikov, Evgueni E.; Xanthis, Leonidas S.: Successive eigenvalue relaxation: A new method for the generalized eigenvalue problem and convergence estimates (2001)
  4. Ron, Amos; Shen, Zuowei; Toh, Kim-Chuan: Computing the Sobolev regularity of refinable functions by the Arnoldi method (2001)
  5. Shepard, Ron; Wagner, Albert F.; Tilson, Jeffrey L.; Minkoff, Michael: The subspace projected approximate matrix (SPAM) modification of the Davidson method (2001)
  6. Stewart, G. W.: A Krylov--Schur algorithm for large eigenproblems (2001)
  7. Wright, Thomas G.; Trefethen, Lloyd N.: Large-scale computation of pseudospectra using ARPACK and eigs (2001)
  8. 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)
  9. Bergamaschi, Luca; Pini, Giorgio; Sartoretto, Flavio: Approximate inverse preconditioning in the parallel solution of sparse eigenproblems (2000)
  10. Golub, Gene H.; van der Vorst, Henk A.: Eigenvalue computation in the 20th century (2000)
  11. Golub, Gene H.; Zhang, Zhenyue; Zha, Hongyuan: Large sparse symmetric eigenvalue problems with homogeneous linear constraints: The Lanczos process with inner-outer iterations (2000)
  12. Morgan, Ronald B.: Implicitly restarted GMRES and Arnoldi methods for nonsymmetric systems of equations (2000)
  13. Morgan, Ronald B.: Preconditioning eigenvalues and some comparison of solvers (2000)
  14. Ruhe, A.: The rational Krylov algorithm for nonlinear matrix eigenvalue problems (2000)
  15. Sameh, Ahmed; Tong, Zhanye: The trace minimization method for the symmetric generalized eigenvalue problem (2000)
  16. Wu, Kesheng; Simon, Horst: Thick-restart Lanczos method for large symmetric eigenvalue problems (2000)
  17. Bai, Zhaojun; Day, David; Ye, Qiang: ABLE: An adaptive block Lanczos method for non-Hermitian eigenvalue problems (1999)
  18. Dohlus, M.; Schuhmann, R.; Weiland, T.: Calculation of frequency domain parameters using 3D eigensolutions (1999)
  19. Elsner, Ulrich; Mehrmann, Volker; Milde, Frank; Römer, Rudolf A.; Schreiber, Michael: The Anderson model of localization: A challenge for modern eigenvalue methods (1999)
  20. Engelborghs, Koen; Roose, Dirk: Numerical computation of stability and detection of Hopf bifurcations of steady state solutions of delay differential equations (1999)

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