eigs: Largest eigenvalues and eigenvectors of matrix The author describes and analyses a new implementation of the Arnoldi method for computing a few eigenvalues and the corresponding eigenvectors of a large general square matrix (which reduces to the Lanczos method in the symmetric case). Using a truncated variant of the implicitly shifted QR-iteration, the author applies a polynomial filter to the Arnoldi (Lanczos) vector on each iteration. This approach generalizes explicit restart methods. Advantages of the method are discussed and some preliminary computational results using parallel and vector computers are given.

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  1. Onunwor, Enyinda; Reichel, Lothar: On the computation of a truncated SVD of a large linear discrete ill-posed problem (2017)
  2. Zhang, Zhongming Teng Lei-Hong: A block Lanczos method for the linear response eigenvalue problem (2017)
  3. Zwaan, Ian N.; Hochstenbach, Michiel E.: Krylov-Schur-type restarts for the two-sided Arnoldi method (2017)
  4. Astudillo, R.; van Gijzen, M. B.: A restarted induced dimension reduction method to approximate eigenpairs of large unsymmetric matrices (2016)
  5. Guglielmi, Nicola; Manetta, Manuela: An iterative method for computing robustness of polynomial stability (2016)
  6. Maroulas, John; Katsouleas, Georgios: Block imbedding and interlacing results for normal matrices (2016)
  7. Pranić, Miroslav S.; Reichel, Lothar; Rodriguez, Giuseppe; Wang, Zhengsheng; Yu, Xuebo: A rational Arnoldi process with applications. (2016)
  8. Shi, Zhanwen; Yang, Guanyu; Xiao, Yunhai: A limited memory BFGS algorithm for non-convex minimization with applications in matrix largest eigenvalue problem (2016)
  9. Zhou, Yunkai; Wang, Zheng; Zhou, Aihui: Accelerating large partial EVD/SVD calculations by filtered block Davidson methods (2016)
  10. Brandts, Jan H.; Reis da Silva, Ricardo: On the subspace projected approximate matrix method. (2015)
  11. Bujanović, Zvonimir; Drmač, Zlatko: A new framework for implicit restarting of the Krylov-Schur algorithm. (2015)
  12. Feng, Ting-Ting; Wu, Gang; Xu, Ting-Ting: An inexact shift-and-invert Arnoldi algorithm for large non-Hermitian generalised Toeplitz eigenproblems (2015)
  13. Harbrecht, Helmut; Peters, Michael; Siebenmorgen, Markus: Efficient approximation of random fields for numerical applications. (2015)
  14. Jia, Zhongxiao; Lv, Hui: A posteriori error estimates of Krylov subspace approximations to matrix functions (2015)
  15. Khazaee, Adib; Lotfi, Vahid: A new technique for determining coupled modes of structure-acoustic systems (2015)
  16. Meerbergen, Karl; Plestenjak, Bor: A Sylvester-Arnoldi type method for the generalized eigenvalue problem with two-by-two operator determinants. (2015)
  17. Plestenjak, Bor; Gheorghiu, Călin I.; Hochstenbach, Michiel E.: Spectral collocation for multiparameter eigenvalue problems arising from separable boundary value problems (2015)
  18. Rostami, Minghao W.: New algorithms for computing the real structured pseudospectral abscissa and the real stability radius of large and sparse matrices (2015)
  19. Salas, Pablo; Giraud, Luc; Saad, Yousef; Moreau, Stéphane: Spectral recycling strategies for the solution of nonlinear eigenproblems in thermoacoustics. (2015)
  20. Shahzadeh Fazeli, S. A.; Emad, Nahid; Liu, Zifan: A key to choose subspace size in implicitly restarted Arnoldi method (2015)

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