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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

A generalized Lánczos scheme


Author: H. A. van der Vorst
Journal: Math. Comp. 39 (1982), 559-561
MSC: Primary 65F15
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] Olof Widlund, A Lanczos method for a class of nonsymmetric systems of linear equations, SIAM J. Numer. Anal. 15 (1978), no. 4, 801–812. MR 0483345 (58 #3357)
  • [2] C. C. Paige, Computational variants of the Lanczos method for the eigenproblem, J. Inst. Math. Appl. 10 (1972), 373–381. MR 0334480 (48 #12799)
  • [3] Jane Cullum and R. A. Willoughby, Fast modal analysis of large, sparse but unstructured symmetric matrices, Proceedings of the 1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes (San Diego, Calif., 1979), IEEE, New York, 1979, pp. 45–53. MR 551854 (81b:65032)
  • [4] B. N. Parlett and J. K. Reid, Tracking the progress of the Lanczos algorithm for large symmetric eigenproblems, IMA J. Numer. Anal. 1 (1981), no. 2, 135–155. MR 616327 (82e:65039), http://dx.doi.org/10.1093/imanum/1.2.135
  • [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: http://dx.doi.org/10.1090/S0025-5718-1982-0669648-0
PII: S 0025-5718(1982)0669648-0
Article copyright: © Copyright 1982 American Mathematical Society