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. Baglama, James; Bella, Tom; Picucci, Jennifer: Hybrid iterative refined method for computing a few extreme eigenpairs of a symmetric matrix (2021)
  2. Baglama, James; Bella, Tom; Picucci, Jennifer: Hybrid iterative refined method for computing a few extreme eigenpairs of a symmetric matrix (2021)
  3. Gradusov, Vitaly A.; Roudnev, Vladimir A.; Yarevsky, Evgeny A.; Yakovlev, Sergey L.: Solving the Faddeev-Merkuriev equations in total orbital momentum representation via spline collocation and tensor product preconditioning (2021)
  4. Hu, Qian-Ying; Wen, Chun; Huang, Ting-Zhu; Shen, Zhao-Li; Gu, Xian-Ming: A variant of the Power-Arnoldi algorithm for computing PageRank (2021)
  5. Steel, Thijs; Camps, Daan; Meerbergen, Karl; Vandebril, Raf: A multishift, multipole rational QZ method with aggressive early deflation (2021)
  6. Wen, Jie; Sun, Huijie; Fei, Lunke; Li, Jinxing; Zhang, Zheng; Zhang, Bob: Consensus guided incomplete multi-view spectral clustering (2021)
  7. Miao, Cun-Qiang: On Chebyshev-Davidson method for symmetric generalized eigenvalue problems (2020)
  8. Wang, Qing-Wen; Wang, Xiang-Xiang: Arnoldi method for large quaternion right eigenvalue problem (2020)
  9. Benner, Peter; Mitchell, Tim: Extended and improved criss-cross algorithms for computing the spectral value set abscissa and radius (2019)
  10. Camps, Daan; Meerbergen, Karl; Vandebril, Raf: A rational QZ method (2019)
  11. Camps, Daan; Meerbergen, Karl; Vandebril, Raf: An implicit filter for rational Krylov using core transformations (2019)
  12. Choi, Young-Geun; Lim, Johan; Roy, Anindya; Park, Junyong: Fixed support positive-definite modification of covariance matrix estimators via linear shrinkage (2019)
  13. Dax, Achiya: Computing the smallest singular triplets of a large matrix (2019)
  14. Dong, Yiqiu; Hansen, Per Christian; Hochstenbach, Michiel E.; Brogaard Riis, Nicolai André: Fixing nonconvergence of algebraic iterative reconstruction with an unmatched backprojector (2019)
  15. Grote, Marcus J.; Nahum, Uri: Adaptive eigenspace for multi-parameter inverse scattering problems (2019)
  16. Hou, Thomas Y.; Huang, De; Lam, Ka Chun; Zhang, Ziyun: A fast hierarchically preconditioned eigensolver based on multiresolution matrix decomposition (2019)
  17. Jia, Zhigang; Ng, Michael K.; Song, Guang-Jing: Lanczos method for large-scale quaternion singular value decomposition (2019)
  18. Miao, Cun-Qiang: Filtered Krylov-like sequence method for symmetric eigenvalue problems (2019)
  19. Noschese, Silvia; Reichel, Lothar: Computing unstructured and structured polynomial pseudospectrum approximations (2019)
  20. Sogaro, Francesca M.; Schmid, Peter J.; Morgans, Aimee S.: Thermoacoustic interplay between intrinsic thermoacoustic and acoustic modes: non-normality and high sensitivities (2019)

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