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On error bounds in strong approximations for eigenvalue problems

Published online by Cambridge University Press:  17 February 2009

R. P. Kulkarani  and
B. V. Limaye
R. P. Kulkarani
Affiliation:
Department of Mathematics, Indian Institute of Technology, Powai, Bombay 400076, India
B. V. Limaye
Affiliation:
Department of Mathematics, Indian Institute of Technology, Powai, Bombay 400076, India
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Abstract

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Some corrections of error bounds obtained by Chatelin and Lemordant for the first three terms of the asymptotic case of a strong approximation are given. The error bounds for the approximations of order 2 in the Galerkin method are compared with the Rayleigh quotients constructed with the eigenvectors in the Sloan method. A numerical experiment is also carried out.

Type
Research Article
Information
The ANZIAM Journal , Volume 22 , Issue 3 , January 1981 , pp. 270 - 283
Copyright
Copyright © Australian Mathematical Society 1981

References

[1]Anselone, P. M., Collectively compact operator approximation theory (Prentice-Hall, New Jersey, 1971).Google Scholar
[2]Chatelin, F. and Lemordant, J., “Error bounds in the approximation of eigenvalues of differential and integral operators”, Report No. STAN-CS-75-479, Stanford University (1975).Google Scholar
[3]Chatelin, F., Linear spectral approximation in Banach spaces (Academic Press, New York), to appear.Google Scholar
[4]Chatelin, F. and Lemordant, J., “Error bounds in the approximation of eigenvalues of differential and integral operators”, J. Math. Anal, and Appl. 62 (1978), 257–271.CrossRefGoogle Scholar
[5]Chatelin, F., “Numerical computation of the eigenelements of linear integral operators by iterations”, SIAM J. Numer. Anal. 15 (1978), 1112–1124.CrossRefGoogle Scholar
[6]Kato, T., “On the upper and lower bounds for eigenvalues”, J. Phys. Soc. Japan 4 (1949), 334–339.CrossRefGoogle Scholar
[7]Kato, T., Perturbation theory for linear operators (Springer-Verlag, Berlin, 1966).Google Scholar
[8]Sloan, I. H., “Iterated Galerkin method for eigenvalue problems”, SIAM J. Numer. Anal. 13 (1976), 753–760.CrossRefGoogle Scholar