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Mathematics of Computation

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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?)

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  • C. C. Paige, Computational variants of the Lanczos method for the eigenproblem, J. Inst. Math. Appl. 10 (1972), 373–381. MR 334480
  • 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
  • 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, DOI
  • 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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Article copyright: © Copyright 1982 American Mathematical Society