eigs

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.


References in zbMATH (referenced in 299 articles , 1 standard article )

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  1. Camps, Daan; Meerbergen, Karl; Vandebril, Raf: An implicit filter for rational Krylov using core transformations (2019)
  2. Hou, Thomas Y.; Huang, De; Lam, Ka Chun; Zhang, Ziyun: A fast hierarchically preconditioned eigensolver based on multiresolution matrix decomposition (2019)
  3. Noschese, Silvia; Reichel, Lothar: Computing unstructured and structured polynomial pseudospectrum approximations (2019)
  4. Bosner, Nela; Bujanović, Zvonimir; Drmač, Zlatko: Parallel solver for shifted systems in a hybrid CPU-GPU framework (2018)
  5. Hack, M. J. Philipp; Moin, Parviz: Coherent instability in wall-bounded shear (2018)
  6. Huang, R.; Sun, J.; Yang, C.: Recursive integral method with Cayley transformation. (2018)
  7. Krämer, Lukas; Lang, Bruno: Convergence of integration-based methods for the solution of standard and generalized Hermitian eigenvalue problems (2018)
  8. Ma, Lingling; Jiang, Lijian: Convergence analysis for GMsFEM approximation of elliptic eigenvalue problems (2018)
  9. Niu, Datian; Meng, Jiana; Li, Hongying: A new shift strategy for the implicitly restarted refined harmonic Lanczos method (2018)
  10. Patanè, G.: Laplacian spectral basis functions (2018)
  11. Rostami, Minghao W.; Xue, Fei: Robust linear stability analysis and a new method for computing the action of the matrix exponential (2018)
  12. Aishima, Kensuke: On convergence of iterative projection methods for symmetric eigenvalue problems (2017)
  13. Che, Maolin; Li, Guoyin; Qi, Liqun; Wei, Yimin: Pseudo-spectra theory of tensors and tensor polynomial eigenvalue problems (2017)
  14. Embree, Mark; Keeler, Blake: Pseudospectra of matrix pencils for transient analysis of differential-algebraic equations (2017)
  15. Grote, Marcus J.; Kray, Marie; Nahum, Uri: Adaptive eigenspace method for inverse scattering problems in the frequency domain (2017)
  16. Gu, Chuanqing; Wang, Wenwen: An Arnoldi-Inout algorithm for computing PageRank problems (2017)
  17. Hou, Thomas Y.; Li, Qin; Zhang, Pengchuan: A sparse decomposition of low rank symmetric positive semidefinite matrices (2017)
  18. Kao, Chiu-Yen; Lai, Rongjie; Osting, Braxton: Maximization of Laplace-Beltrami eigenvalues on closed Riemannian surfaces (2017)
  19. Miao, Cun-Qiang: A filtered-Davidson method for large symmetric eigenvalue problems (2017)
  20. Noschese, Silvia; Reichel, Lothar: Approximated structured pseudospectra. (2017)

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