JDQZ

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.

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

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  1. Voss, H.: A projection method for a rational eigenvalue problem in fluid-structure interaction (2002)
  2. Dijkstra, Henk A.; Oksuzoglu, Hakan; Wubs, Fred. W.; Botta, Eugen F. F.: A fully implicit model of the three-dimensional thermohaline ocean circulation (2001)
  3. Freund, Roland W.: Computation of matrix-valued formally orthogonal polynomials and applications (2001)
  4. Im, Eun-Jin; Yelick, Katherine: Optimizing sparse matrix computations for register reuse in SPARSITY (2001)
  5. Jia, Zhongxiao: Residuals of refined projection methods for large matrix eigenproblems (2001)
  6. Jia, Zhongxiao; Stewart, G. W.: An analysis of the Rayleigh-Ritz method for approximating eigenspaces (2001)
  7. Knyazev, Andrew V.: Toward the optimal preconditioned eigensolver: Locally optimal block preconditioned conjugate gradient method (2001)
  8. Lehoucq, R. B.: Implicitly restarted Arnoldi methods and subspace iteration (2001)
  9. Meerbergen, Karl: Locking and restarting quadratic eigenvalue solvers (2001)
  10. Mehrmann, Volker; Watkins, David: Structure-preserving methods for computing eigenpairs of large sparse skew-Hamiltonian/Hamiltonian pencils (2001)
  11. Ovtchinnikov, Evgueni E.; Xanthis, Leonidas S.: Successive eigenvalue relaxation: A new method for the generalized eigenvalue problem and convergence estimates (2001)
  12. Ron, Amos; Shen, Zuowei; Toh, Kim-Chuan: Computing the Sobolev regularity of refinable functions by the Arnoldi method (2001)
  13. Shepard, Ron; Wagner, Albert F.; Tilson, Jeffrey L.; Minkoff, Michael: The subspace projected approximate matrix (SPAM) modification of the Davidson method (2001)
  14. Stewart, G. W.: A Krylov--Schur algorithm for large eigenproblems (2001)
  15. Wright, Thomas G.; Trefethen, Lloyd N.: Large-scale computation of pseudospectra using ARPACK and eigs (2001)
  16. 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)
  17. Bergamaschi, Luca; Pini, Giorgio; Sartoretto, Flavio: Approximate inverse preconditioning in the parallel solution of sparse eigenproblems (2000)
  18. Golub, Gene H.; van der Vorst, Henk A.: Eigenvalue computation in the 20th century (2000)
  19. Golub, Gene H.; Zhang, Zhenyue; Zha, Hongyuan: Large sparse symmetric eigenvalue problems with homogeneous linear constraints: The Lanczos process with inner-outer iterations (2000)
  20. Morgan, Ronald B.: Implicitly restarted GMRES and Arnoldi methods for nonsymmetric systems of equations (2000)

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