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A hierarchical method for obtaining eigenvalue enclosures
Author(s):
E.
B.
Davies.
Journal:
Math. Comp.
69
(2000),
1435-1455.
MSC (1991):
Primary 34L15, 35P15, 49R05, 49R10, 65L15, 65L60, 65L70, 65N25
Posted:
March 6, 2000
MathSciNet review:
1710648
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Abstract:
We introduce a new method of obtaining guaranteed enclosures of the eigenvalues of a variety of self-adjoint differential and difference operators with discrete spectrum. The method is based upon subdividing the region into a number of simpler regions for which eigenvalue enclosures are already available.
References:
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- 2.
- E B Davies. Spectral Theory and Differential Operators. Cambridge Univ. Press, 1995. MR 96h:47056
- 3.
- E B Davies. Spectral enclosures and complex resonances for general self-adjoint operators. LMS J. Comput. Math. 1 (1998) 42-74. CMP 98:15
- 4.
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- 5.
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- 6.
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- 9.
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- 11.
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MSC (1991):
34L15, 35P15, 49R05, 49R10, 65L15, 65L60, 65L70, 65N25
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MSC (1991):
34L15, 35P15, 49R05, 49R10, 65L15, 65L60, 65L70, 65N25
Additional Information:
E.
B.
Davies
Affiliation:
Department of Mathematics, King's College, Strand, London, WC2R 2LS, United Kingdom
Email:
E.Brian.Davies@kcl.ac.uk
DOI:
10.1090/S0025-5718-00-01238-2
PII:
S 0025-5718(00)01238-2
Keywords:
Spectrum,
eigenvalues,
spectral enclosures,
interval arithmetic,
Rayleigh-Ritz method,
Temple-Lehmann method
Received by editor(s):
October 27, 1998
Posted:
March 6, 2000
Copyright of article:
Copyright
2000,
American Mathematical Society
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