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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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A generalized Lánczos scheme
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by H. A. van der Vorst PDF
Math. Comp. 39 (1982), 559-561 Request permission

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
  • 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 483345, DOI 10.1137/0715053
  • C. C. Paige, Computational variants of the Lanczos method for the eigenproblem, J. Inst. Math. Appl. 10 (1972), 373–381. MR 334480, DOI 10.1093/imamat/10.3.373
  • 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 10.1093/imanum/1.2.135
  • 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
  • © Copyright 1982 American Mathematical Society
  • Journal: Math. Comp. 39 (1982), 559-561
  • MSC: Primary 65F15
  • DOI: https://doi.org/10.1090/S0025-5718-1982-0669648-0
  • MathSciNet review: 669648