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The Quasi-Laguerre iteration

Author(s): Qiang Du; Ming Jin; T. Y. Li; Z. Zeng.
Journal: Math. Comp. 66 (1997), 345-361.
MSC (1991): Primary 65F15; Secondary 65F40
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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:

1.
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.

2.
L. V. Foster, Generalizations of Laguerre's method: lower order methods, preprint.

3.
W. Kahan, Notes On Laguerre's Iteration,

preprint, University of California, Berkeley (1992).

4.
T. Y. Li and Z. Zeng, The Laguerre iteration in solving the symmetric tridiagonal eigenproblem - revisited,

SIAM J. Sci. Comput. 15 (1994), 1145-1173. MR 95h:65024

5.
J. H. Wilkinson, The algebraic eigenvalue problem, Clarendon Press, Oxford, England, 1965.MR 32:1894

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Additional Information:

Qiang Du
Affiliation: Department of Mathematics, Michigan State University, East Lansing, Michigan 48824
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
Email: uzzeng@uxa.ecn.bgu.edu

DOI: 10.1090/S0025-5718-97-00786-2
PII: S 0025-5718(97)00786-2
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 of article: Copyright 1997, American Mathematical Society

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