Implicitly restarted Arnoldi methods and subspace iteration

SIAM Journal on Matrix Analysis and Applications

Volumn 23, Issue 2, 2002, Pages 551-562

  Lehoucq, R B ^a  

^a SANDIA NATIONAL LABORATORIES   (United States)

Author keywords

Arnoldi reduction; Eigenvalues; Restarting; Schur decomposition; Simultaneous iteration

Indexed keywords

EID: 0036058969     PISSN: 08954798     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0895479899358595     Document Type: Article

References (41)

1. The principle of minimized iterations in the solution of the matrix eigenvalue problem
2. Iterative methods for the computation of a few eigenvalues of a large symmetric matrix
3. Fast Leja points
4. Computation of a few close eigenvalues of a large matrix with application to liquid crystal modeling
5. SRRIT - A FORTRAN subroutine to calculate the dominant invariant subspace of a nonsymmetric matrix
6. Das verfahren der treppeniteration und verwandte verfahren zur losung algebraischer eigenwertproblem
7. Computing selected eigenvalues of large sparse unsymmetric matrices using subspace iteration
8. Ill-conditioned eigensystems and the computation of the Jordan canonical form
9. A shifted block Lanczos algorithm for solving sparse symmetric generalized eigenproblems
10. The convergence of generalized Lanczos methods for large unsymmetric eigenproblems
11. Generalized block Lanczos methods for large unsymmetric eigenproblems
12. Polynomial characterizations of the approximate eigenvectors by the refined Arnoldi method and an implicitly restarted refined Arnoldi algorithm
13. An iteration method for the solution of the eigenvalue problem of linear differential and integral operators
14. Block Arnoldi method
15. Implicitly restarted Arnoldi with purification for the shift-invert transformation
16. Harmonic projection methods for large non-symmetric eigenvalue problems
17. Computing interior eigenvalues of large matrices
18. On restarting the Arnoldi method for large nonsymmetric eigenvalue problems
19. Approximate solutions and eigenvalue bounds from Krylov subspaces
20. Computational aspects of F.L. Bauer's simultaneous iteration method for symmetric matrices
21. Simultaneous iteration method for symmetric matrices
22. Variations on Arnoldi's method for computing eigenelements of large unsymmetric matrices
23. Chebyshev acceleration techniques for solving nonsymmetric eigenvalue problems
24. A block Arnoldi-Chebyshev method for computing the leading eigenpairs of large sparse unsymmetric matrices
25. An Arnoldi code for computing selected eigenvalues of sparse real unsymmetric matrices
26. A Jacobi-Davidson iteration method for linear eigenvalue problems
27. Matrix eigensystem routines - EISPACK guide, 2nd ed.
28. Implicit application of polynomial filters in a k-step Arnoldi method
29. Dynamic thick restarting of the Davidson, and the implicitly restarted Arnoldi methods
30. Accelerating the orthogonal iteration for the eigenvectors of a Hermitian matrix
31. Simultaneous iteration for computing invariant subspaces of non-Hermitian matrices
32. Understanding the QR algorithm
33. Convergence of algorithms of decomposition type for the eigenvalue problem
34. Modified explicitly restarted Lanczos algorithm