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A generalized Lánczos scheme


Author: H. A. van der Vorst
Journal: Math. Comp. 39 (1982), 559-561
MSC: Primary 65F15
DOI: https://doi.org/10.1090/S0025-5718-1982-0669648-0
MathSciNet review: 669648
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Abstract: It is shown in this paper how the Lanczos algorithm can be generalized so that it applies to both symmetric and skew-symmetric matrices and corresponding generalized eigenvalue problems.


References [Enhancements On Off] (What's this?)

  • [1] O. Widlund, "A Lanczos method for a class of non-symmetric systems of linear equations," SIAM J. Numer. Anal., v. 15, 1978, pp. 801-812. MR 0483345 (58:3357)
  • [2] C. C. Paige, "Computational variants of the Lanczos method for the eigenproblem," J. Inst. Math. Appl., v. 10, 1972, pp. 373-381. MR 0334480 (48:12799)
  • [3] J. Cullum & R. A. Willoughby, "Fast modal analysis of large, sparse but unstructured symmetric matrices," Proc. 17th IEEE Conf. on Decision and Control, 1979. MR 551854 (81b:65032)
  • [4] B. Parlett & J. K. Reid, "Tracking the progress of the Lanczos algorithm for large symmetric eigenproblems," IMA J. Numer. Anal., v. 1, 1981, pp. 135-155. MR 616327 (82e:65039)
  • [5] J. M. van Kats & H. A. van der Vorst, Automatic Monitoring of Lanczos Schemes for Symmetric or Skew-Symmetric Generalized Eigenvalue Problems. Technical report TR-7, Academisch Computer Centrum Utrecht, 1977.

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1982-0669648-0
Article copyright: © Copyright 1982 American Mathematical Society

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