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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  1. Adachi, Satoru; Iwata, Satoru; Nakatsukasa, Yuji; Takeda, Akiko: Solving the trust-region subproblem by a generalized eigenvalue problem (2017)
  2. Betcke, Marta M.; Voss, Heinrich: Restarting iterative projection methods for Hermitian nonlinear eigenvalue problems with minmax property (2017)
  3. Nakatsukasa, Yuji; Soma, Tasuku; Uschmajew, André: Finding a low-rank basis in a matrix subspace (2017)
  4. Breuer, Alex; Lumsdaine, Andrew: Matrix-free Krylov iteration for implicit convolution of numerically low-rank data (2016)
  5. Brown, Kirsty L.; Gejadze, Igor; Ramage, Alison: A multilevel approach for computing the limited-memory Hessian and its inverse in variational data assimilation (2016)
  6. Campos, Carmen; Roman, Jose E.: Restarted Q-Arnoldi-type methods exploiting symmetry in quadratic eigenvalue problems (2016)
  7. Campos, Carmen; Roman, Jose E.: Parallel Krylov solvers for the polynomial eigenvalue problem in SLEPc (2016)
  8. Chorowski, Jakub; Trabs, Mathias: Spectral estimation for diffusions with random sampling times (2016)
  9. Gaudreau, P.; Slevinsky, R.; Safouhi, H.: The double exponential sinc collocation method for singular Sturm-Liouville problems (2016)
  10. Giani, Stefano; Grubišić, Luka; Międlar, Agnieszka; Ovall, Jeffrey S.: Robust error estimates for approximations of non-self-adjoint eigenvalue problems (2016)
  11. Higham, Nicholas J.; Strabić, Nataša: Bounds for the distance to the nearest correlation matrix (2016)
  12. Huang, Tsung-Ming; Lin, Wen-Wei; Mehrmann, Volker: A Newton-type method with nonequivalence deflation for nonlinear eigenvalue problems arising in photonic crystal modeling (2016)
  13. Imbrie, John Z.: Multi-scale Jacobi method for Anderson localization (2016)
  14. Imbrie, John Z.: On many-body localization for quantum spin chains (2016)
  15. Michaud-Rioux, Vincent; Zhang, Lei; Guo, Hong: RESCU: a real space electronic structure method (2016)
  16. Nakatsukasa, Yuji; Freund, Roland W.: Computing fundamental matrix decompositions accurately via the matrix sign function in two iterations: the power of Zolotarev’s functions (2016)
  17. Neymeyr, Klaus; Zhou, Ming: Convergence analysis of restarted Krylov subspace eigensolvers (2016)
  18. Palacios, José Luis; Quiroz, Daniel: Birth and death chains on finite trees: computing their stationary distribution and hitting times (2016)
  19. Schröder, Christian; Taslaman, Leo: Backward error analysis of the shift-and-invert Arnoldi algorithm (2016)
  20. Shi, Zhanwen; Yang, Guanyu; Xiao, Yunhai: A limited memory BFGS algorithm for non-convex minimization with applications in matrix largest eigenvalue problem (2016)

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