Implicit application of polynomial filters in a k-step Arnoldi method. 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. Hack, M. J. Philipp; Moin, Parviz: Coherent instability in wall-bounded shear (2018)
  2. Ma, Lingling; Jiang, Lijian: Convergence analysis for GMsFEM approximation of elliptic eigenvalue problems (2018)
  3. Niu, Datian; Meng, Jiana; Li, Hongying: A new shift strategy for the implicitly restarted refined harmonic Lanczos method (2018)
  4. Aishima, Kensuke: On convergence of iterative projection methods for symmetric eigenvalue problems (2017)
  5. Bosch, Jessica; Greif, Chen: Numerical solution of linear eigenvalue problems (2017)
  6. Gu, Chuanqing; Wang, Wenwen: An Arnoldi-Inout algorithm for computing PageRank problems (2017)
  7. Hou, Thomas Y.; Li, Qin; Zhang, Pengchuan: A sparse decomposition of low rank symmetric positive semidefinite matrices (2017)
  8. Kao, Chiu-Yen; Lai, Rongjie; Osting, Braxton: Maximization of Laplace-Beltrami eigenvalues on closed Riemannian surfaces (2017)
  9. Lloyd, David J. B.; Scheel, Arnd: Continuation and bifurcation of grain boundaries in the Swift-Hohenberg equation (2017)
  10. Miao, Cun-Qiang: A filtered-Davidson method for large symmetric eigenvalue problems (2017)
  11. Onunwor, Enyinda; Reichel, Lothar: On the computation of a truncated SVD of a large linear discrete ill-posed problem (2017)
  12. Astudillo, R.; van Gijzen, M. B.: A restarted induced dimension reduction method to approximate eigenpairs of large unsymmetric matrices (2016)
  13. Katsouleas, Georgios; Maroulas, John: An inverse problem for the $k$-rank numerical range (2016)
  14. Kestyn, James; Polizzi, Eric; Tang, Ping Tak Peter: Feast eigensolver for non-Hermitian problems (2016)
  15. Maroulas, John; Katsouleas, Georgios: Block imbedding and interlacing results for normal matrices (2016)
  16. Zhou, Yunkai; Wang, Zheng; Zhou, Aihui: Accelerating large partial EVD/SVD calculations by filtered block Davidson methods (2016)
  17. Aishima, Kensuke: Global convergence of the restarted Lanczos and Jacobi-Davidson methods for symmetric eigenvalue problems (2015)
  18. Brandts, Jan H.; Reis da Silva, Ricardo: On the subspace projected approximate matrix method. (2015)
  19. Bujanović, Zvonimir; Drmač, Zlatko: A new framework for implicit restarting of the Krylov-Schur algorithm. (2015)
  20. Dookhitram, Kumar; Tangman, Yannick Désiré; Bhuruth, Muddun: Convergence of Arnoldi’s method for generalized eigenvalue problems (2015)

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