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Galerkin eigenvector approximations
Author(s):
Christopher
Beattie.
Journal:
Math. Comp.
69
(2000),
1409-1434.
MSC (1991):
Primary 65N25;
Secondary 65N30, 65F15
Posted:
March 3, 2000
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Abstract:
How close are Galerkin eigenvectors to the best approximation available out of the trial subspace? Under a variety of conditions the Galerkin method gives an approximate eigenvector that approaches asymptotically the projection of the exact eigenvector onto the trial subspace--and this occurs more rapidly than the underlying rate of convergence of the approximate eigenvectors. Both orthogonal-Galerkin and Petrov-Galerkin methods are considered here with a special emphasis on nonselfadjoint problems, thus extending earlier studies by Chatelin, Babuska and Osborn, and Knyazev. Consequences for the numerical treatment of elliptic PDEs discretized either with finite element methods or with spectral methods are discussed. New lower bounds to the  of a pair of operators are developed as well.
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Additional Information:
Christopher
Beattie
Affiliation:
Department of Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061 USA
Email:
beattie@math.vt.edu
DOI:
10.1090/S0025-5718-00-01181-9
PII:
S 0025-5718(00)01181-9
Keywords:
Galerkin,
eigenvector asymptotics,
finite elements,
spectral methods,
\textit{sep}.
Received by editor(s):
January 6, 1998
Received by editor(s) in revised form:
July 10, 1998 and October 9, 1998
Posted:
March 3, 2000
Additional Notes:
This work was supported under the auspices of AFOSR Grant F49620-96-1-0329
Copyright of article:
Copyright
2000,
American Mathematical Society
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