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. Gu, Chuanqing; Wang, Wenwen: An Arnoldi-Inout algorithm for computing PageRank problems (2017)
  2. Hou, Thomas Y.; Li, Qin; Zhang, Pengchuan: A sparse decomposition of low rank symmetric positive semidefinite matrices (2017)
  3. Kao, Chiu-Yen; Lai, Rongjie; Osting, Braxton: Maximization of Laplace-Beltrami eigenvalues on closed Riemannian surfaces (2017)
  4. Lloyd, David J.B.; Scheel, Arnd: Continuation and bifurcation of grain boundaries in the Swift-Hohenberg equation (2017)
  5. Astudillo, R.; van Gijzen, M.B.: A restarted induced dimension reduction method to approximate eigenpairs of large unsymmetric matrices (2016)
  6. Katsouleas, Georgios; Maroulas, John: An inverse problem for the $k$-rank numerical range (2016)
  7. Kestyn, James; Polizzi, Eric; Tang, Ping Tak Peter: Feast eigensolver for non-Hermitian problems (2016)
  8. Maroulas, John; Katsouleas, Georgios: Block imbedding and interlacing results for normal matrices (2016)
  9. Zhou, Yunkai; Wang, Zheng; Zhou, Aihui: Accelerating large partial EVD/SVD calculations by filtered block Davidson methods (2016)
  10. Aishima, Kensuke: Global convergence of the restarted Lanczos and Jacobi-Davidson methods for symmetric eigenvalue problems (2015)
  11. Brandts, Jan H.; Reis da Silva, Ricardo: On the subspace projected approximate matrix method. (2015)
  12. Dookhitram, Kumar; Tangman, Yannick Désiré; Bhuruth, Muddun: Convergence of Arnoldi’s method for generalized eigenvalue problems (2015)
  13. Jia, Zhongxiao; Lin, Wen-Wei; Liu, Ching-Sung: A positivity preserving inexact Noda iteration for computing the smallest eigenpair of a large irreducible $M$-matrix (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. Plestenjak, Bor; Gheorghiu, Călin I.; Hochstenbach, Michiel E.: Spectral collocation for multiparameter eigenvalue problems arising from separable boundary value problems (2015)
  17. Rostami, Minghao W.: New algorithms for computing the real structured pseudospectral abscissa and the real stability radius of large and sparse matrices (2015)
  18. Shahzadeh Fazeli, S.A.; Emad, Nahid; Liu, Zifan: A key to choose subspace size in implicitly restarted Arnoldi method (2015)
  19. Duintjer Tebbens, Jurjen; Meurant, Gérard: Prescribing the behavior of early terminating GMRES and Arnoldi iterations (2014)
  20. Katsouleas, Georgios; Maroulas, John: Interaction between Hermitian and normal imbeddings (2014)

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