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. Ma, Lingling; Jiang, Lijian: Convergence analysis for GMsFEM approximation of elliptic eigenvalue problems (2018)
  2. Niu, Datian; Meng, Jiana; Li, Hongying: A new shift strategy for the implicitly restarted refined harmonic Lanczos method (2018)
  3. Aishima, Kensuke: On convergence of iterative projection methods for symmetric eigenvalue problems (2017)
  4. Che, Maolin; Li, Guoyin; Qi, Liqun; Wei, Yimin: Pseudo-spectra theory of tensors and tensor polynomial eigenvalue problems (2017)
  5. Embree, Mark; Keeler, Blake: Pseudospectra of matrix pencils for transient analysis of differential-algebraic equations (2017)
  6. Grote, Marcus J.; Kray, Marie; Nahum, Uri: Adaptive eigenspace method for inverse scattering problems in the frequency domain (2017)
  7. Gu, Chuanqing; Wang, Wenwen: An Arnoldi-Inout algorithm for computing PageRank problems (2017)
  8. Hou, Thomas Y.; Li, Qin; Zhang, Pengchuan: A sparse decomposition of low rank symmetric positive semidefinite matrices (2017)
  9. Kao, Chiu-Yen; Lai, Rongjie; Osting, Braxton: Maximization of Laplace-Beltrami eigenvalues on closed Riemannian surfaces (2017)
  10. Miao, Cun-Qiang: A filtered-Davidson method for large symmetric eigenvalue problems (2017)
  11. Noschese, Silvia; Reichel, Lothar: Approximated structured pseudospectra. (2017)
  12. Onunwor, Enyinda; Reichel, Lothar: On the computation of a truncated SVD of a large linear discrete ill-posed problem (2017)
  13. Zhang, Zhongming Teng Lei-Hong: A block Lanczos method for the linear response eigenvalue problem (2017)
  14. Zwaan, Ian N.; Hochstenbach, Michiel E.: Krylov-Schur-type restarts for the two-sided Arnoldi method (2017)
  15. Astudillo, R.; van Gijzen, M.B.: A restarted induced dimension reduction method to approximate eigenpairs of large unsymmetric matrices (2016)
  16. Guglielmi, Nicola; Manetta, Manuela: An iterative method for computing robustness of polynomial stability (2016)
  17. Maroulas, John; Katsouleas, Georgios: Block imbedding and interlacing results for normal matrices (2016)
  18. Pranić, Miroslav S.; Reichel, Lothar; Rodriguez, Giuseppe; Wang, Zhengsheng; Yu, Xuebo: A rational Arnoldi process with applications. (2016)
  19. Shi, Zhanwen; Yang, Guanyu; Xiao, Yunhai: A limited memory BFGS algorithm for non-convex minimization with applications in matrix largest eigenvalue problem (2016)
  20. Zhou, Yunkai; Wang, Zheng; Zhou, Aihui: Accelerating large partial EVD/SVD calculations by filtered block Davidson methods (2016)

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