Bounding Eigenvalues of Elliptic Operators

Bounding Eigenvalues of Elliptic Operators

We present a method which bounds the error between an estimate for a point in the spectrum and an eigenvalue of self-adjoint elliptic operators. The method makes use of trial functions which need not satisfy the boundary conditions of the problem. By using rough preliminary estimates for the eigenva...

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Veröffentlicht in:SIAM journal on mathematical analysis 1978-08, Vol.9 (4), p.768-773
Hauptverfasser: Kuttler, J. R., Sigillito, V. G.
Format: Artikel
Sprache:eng
Schlagworte:
Boundary conditions
Eigenvalues
Eigenvectors
Hilbert space
Inequality
Symmetry
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Zusammenfassung:We present a method which bounds the error between an estimate for a point in the spectrum and an eigenvalue of self-adjoint elliptic operators. The method makes use of trial functions which need not satisfy the boundary conditions of the problem. By using rough preliminary estimates for the eigenvalues this method gives both upper and lower bounds.
ISSN:0036-1410
1095-7154
DOI:10.1137/0509056