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. Yang, Liu; Sun, Yuquan; Gong, Fanghui: The inexact residual iteration method for quadratic eigenvalue problem and the analysis of convergence (2018)
  2. Adachi, Satoru; Iwata, Satoru; Nakatsukasa, Yuji; Takeda, Akiko: Solving the trust-region subproblem by a generalized eigenvalue problem (2017)
  3. Aishima, Kensuke: On convergence of iterative projection methods for symmetric eigenvalue problems (2017)
  4. Antoine, Xavier; Levitt, Antoine; Tang, Qinglin: Efficient spectral computation of the stationary states of rotating Bose-Einstein condensates by preconditioned nonlinear conjugate gradient methods (2017)
  5. Argentati, Merico E.; Knyazev, Andrew V.; Neymeyr, Klaus; Ovtchinnikov, Evgueni E.; Zhou, Ming: Convergence theory for preconditioned eigenvalue solvers in a nutshell (2017)
  6. Bai, Zhong-Zhi; Miao, Cun-Qiang: On local quadratic convergence of inexact simplified Jacobi-Davidson method (2017)
  7. Betcke, Marta M.; Voss, Heinrich: Restarting iterative projection methods for Hermitian nonlinear eigenvalue problems with minmax property (2017)
  8. Lin, Lin: Localized spectrum slicing (2017)
  9. Lu, Jianfeng; Yang, Haizhao: A cubic scaling algorithm for excited states calculations in particle-particle random phase approximation (2017)
  10. Miao, Cun-Qiang: A filtered-Davidson method for large symmetric eigenvalue problems (2017)
  11. Nakatsukasa, Yuji: Accuracy of singular vectors obtained by projection-based SVD methods (2017)
  12. Nakatsukasa, Yuji; Soma, Tasuku; Uschmajew, André: Finding a low-rank basis in a matrix subspace (2017)
  13. Pequito, Sérgio; Ramos, Guilherme; Kar, Soummya; Aguiar, A.Pedro; Ramos, Jaime: The robust minimal controllability problem (2017)
  14. Scott, Tony C.; Therani, Madhusudan; Wang, Xing M.: Data clustering with quantum mechanics (2017)
  15. Wang, Wei-Guo; Wei, Yimin: Mixed and componentwise condition numbers for matrix decompositions (2017)
  16. Wang, Xiang; Tang, Xiao-Bin; Mao, Liang-Zhi: A modified second-order Arnoldi method for solving the quadratic eigenvalue problems (2017)
  17. Wen, Zaiwen; Zhang, Yin: Accelerating convergence by augmented Rayleigh-Ritz projections for large-scale eigenpair computation (2017)
  18. Wu, Gang: The convergence of harmonic Ritz vectors and harmonic Ritz values, revisited (2017)
  19. Wu, Gang; Pang, Hong-Kui: On the correction equation of the Jacobi-Davidson method (2017)
  20. Xiao, Jinyou; Zhou, Hang; Zhang, Chuanzeng; Xu, Chao: Solving large-scale finite element nonlinear eigenvalue problems by resolvent sampling based Rayleigh-Ritz method (2017)

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