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Mathematics of Computation

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

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The quasi-Laguerre iteration
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by Qiang Du, Ming Jin, T. Y. Li and Z. Zeng PDF
Math. Comp. 66 (1997), 345-361 Request permission

Abstract:

The quasi-Laguerre iteration has been successfully established, by the same authors, in the spirit of Laguerre’s iteration for solving the eigenvalues of symmetric tridiagonal matrices. The improvement in efficiency over Laguerre’s iteration is drastic. This paper supplements the theoretical background of this new iteration, including the proofs of the convergence properties.
References
  • Qiang Du, Ming Jin, T.Y. Li and Z. Zeng, Quasi-Laguerre iteration in solving symmetric tridiagonal eigenvalue problems , to appear: SIAM J. Sci. Comput.
  • L. V. Foster, Generalizations of Laguerre’s method: lower order methods, preprint.
  • W. Kahan, Notes On Laguerre’s Iteration, preprint, University of California, Berkeley (1992).
  • T. Y. Li and Zhong Gang Zeng, The Laguerre iteration in solving the symmetric tridiagonal eigenproblem, revisited, SIAM J. Sci. Comput. 15 (1994), no. 5, 1145–1173. MR 1289159, DOI 10.1137/0915071
  • J. H. Wilkinson, The algebraic eigenvalue problem, Clarendon Press, Oxford, 1965. MR 0184422
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Additional Information
  • Qiang Du
  • Affiliation: Department of Mathematics, Michigan State University, East Lansing, Michigan 48824
  • MR Author ID: 191080
  • Email: du@math.msu.edu
  • Ming Jin
  • Affiliation: Department of Mathematics, Michigan State University, East Lansing, Michigan 48824
  • Address at time of publication: Department of Mathematics, Lambuth University, Jackson, Tennessee 38301
  • Email: jinm66@usit.net
  • T. Y. Li
  • Affiliation: Department of Mathematics, Michigan State University, East Lansing, Michigan 48824
  • Email: li@math.msu.edu
  • Z. Zeng
  • Affiliation: Department of Mathematics, Northeastern Illinois University, Chicago, Illinois 60625
  • MR Author ID: 214819
  • ORCID: 0000-0001-8879-8077
  • Email: uzzeng@uxa.ecn.bgu.edu
  • Received by editor(s): August 9, 1995
  • Received by editor(s) in revised form: September 15, 1995
  • Additional Notes: The research of the first author was supported in part by NSF under Grant DMS-9500718.
    The research of the third author was supported in part by NSF under Grant DMS-9504953 and by a Guggenheim Fellowship.
  • © Copyright 1997 American Mathematical Society
  • Journal: Math. Comp. 66 (1997), 345-361
  • MSC (1991): Primary 65F15; Secondary 65F40
  • DOI: https://doi.org/10.1090/S0025-5718-97-00786-2
  • MathSciNet review: 1370851