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. Wang, Qing-Wen; Wang, Xiang-Xiang: Arnoldi method for large quaternion right eigenvalue problem (2020)
  2. Benner, Peter; Mitchell, Tim: Extended and improved criss-cross algorithms for computing the spectral value set abscissa and radius (2019)
  3. Camps, Daan; Meerbergen, Karl; Vandebril, Raf: A rational QZ method (2019)
  4. Camps, Daan; Meerbergen, Karl; Vandebril, Raf: An implicit filter for rational Krylov using core transformations (2019)
  5. Choi, Young-Geun; Lim, Johan; Roy, Anindya; Park, Junyong: Fixed support positive-definite modification of covariance matrix estimators via linear shrinkage (2019)
  6. Dong, Yiqiu; Hansen, Per Christian; Hochstenbach, Michiel E.; Brogaard Riis, Nicolai André: Fixing nonconvergence of algebraic iterative reconstruction with an unmatched backprojector (2019)
  7. Hou, Thomas Y.; Huang, De; Lam, Ka Chun; Zhang, Ziyun: A fast hierarchically preconditioned eigensolver based on multiresolution matrix decomposition (2019)
  8. Jia, Zhigang; Ng, Michael K.; Song, Guang-Jing: Lanczos method for large-scale quaternion singular value decomposition (2019)
  9. Miao, Cun-Qiang: Filtered Krylov-like sequence method for symmetric eigenvalue problems (2019)
  10. Noschese, Silvia; Reichel, Lothar: Computing unstructured and structured polynomial pseudospectrum approximations (2019)
  11. Sogaro, Francesca M.; Schmid, Peter J.; Morgans, Aimee S.: Thermoacoustic interplay between intrinsic thermoacoustic and acoustic modes: non-normality and high sensitivities (2019)
  12. Wu, Lingfei; Xue, Fei; Stathopoulos, Andreas: TRPL+K: thick-restart preconditioned Lanczos+K method for large symmetric eigenvalue problems (2019)
  13. Zadeh, Najmeh Azizi; Tajaddini, Azita; Wu, Gang: Weighted and deflated global GMRES algorithms for solving large Sylvester matrix equations (2019)
  14. Bosner, Nela; Bujanović, Zvonimir; Drmač, Zlatko: Parallel solver for shifted systems in a hybrid CPU-GPU framework (2018)
  15. Bucci, M. A.; Puckert, D. K.; Andriano, C.; Loiseau, J.-C.; Cherubini, S.; Robinet, J.-C.; Rist, U.: Roughness-induced transition by quasi-resonance of a varicose global mode (2018)
  16. Gu, Chuanqing; Jiang, Xianglong; Nie, Ying; Chen, Zhibing: A preprocessed multi-step splitting iteration for computing PageRank (2018)
  17. Hack, M. J. Philipp; Moin, Parviz: Coherent instability in wall-bounded shear (2018)
  18. Huang, R.; Sun, J.; Yang, C.: Recursive integral method with Cayley transformation. (2018)
  19. Krämer, Lukas; Lang, Bruno: Convergence of integration-based methods for the solution of standard and generalized Hermitian eigenvalue problems (2018)
  20. Ma, Lingling; Jiang, Lijian: Convergence analysis for GMsFEM approximation of elliptic eigenvalue problems (2018)

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