IRAM

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


References in zbMATH (referenced in 203 articles )

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  1. Feng, Bo; Wu, Gang: On a new variant of Arnoldi method for approximation of eigenpairs (2022)
  2. Baglama, James; Bella, Tom; Picucci, Jennifer: Hybrid iterative refined method for computing a few extreme eigenpairs of a symmetric matrix (2021)
  3. Baglama, James; Bella, Tom; Picucci, Jennifer: Hybrid iterative refined method for computing a few extreme eigenpairs of a symmetric matrix (2021)
  4. Embree, Mark; Loe, Jennifer A.; Morgan, Ronald: Polynomial preconditioned Arnoldi with stability control (2021)
  5. 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)
  6. Hashemian, Ali; Pardo, David; Calo, Victor M.: Refined isogeometric analysis for generalized Hermitian eigenproblems (2021)
  7. 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)
  8. Miao, Cun-Qiang; Wu, Wen-Ting: On relaxed filtered Krylov subspace method for non-symmetric eigenvalue problems (2021)
  9. Steel, Thijs; Camps, Daan; Meerbergen, Karl; Vandebril, Raf: A multishift, multipole rational QZ method with aggressive early deflation (2021)
  10. Aishima, Kensuke: Convergence proof of the harmonic Ritz pairs of iterative projection methods with restart strategies for symmetric eigenvalue problems (2020)
  11. Dax, Achiya: A cross-product approach for low-rank approximations of large matrices (2020)
  12. Miao, Cun-Qiang: On Chebyshev-Davidson method for symmetric generalized eigenvalue problems (2020)
  13. Polizzi, Eric; Saad, Yousef: Computational materials science and engineering (2020)
  14. Wang, Qing-Wen; Wang, Xiang-Xiang: Arnoldi method for large quaternion right eigenvalue problem (2020)
  15. Camps, Daan; Meerbergen, Karl; Vandebril, Raf: A rational QZ method (2019)
  16. Camps, Daan; Meerbergen, Karl; Vandebril, Raf: An implicit filter for rational Krylov using core transformations (2019)
  17. Choi, Young-Geun; Lim, Johan; Roy, Anindya; Park, Junyong: Fixed support positive-definite modification of covariance matrix estimators via linear shrinkage (2019)
  18. Dax, Achiya: Computing the smallest singular triplets of a large matrix (2019)
  19. Dong, Yiqiu; Hansen, Per Christian; Hochstenbach, Michiel E.; Brogaard Riis, Nicolai André: Fixing nonconvergence of algebraic iterative reconstruction with an unmatched backprojector (2019)
  20. Elman, Howard C.; Su, Tengfei: Low-rank solution methods for stochastic eigenvalue problems (2019)

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