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Zeitschrift für Analysis und ihre Anwendungen


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Volume 15, Issue 3, 1996, pp. 661–686
DOI: 10.4171/ZAA/722

Published online: 1996-09-30

On the Convergence of the Goerisch Method for Self-Adjoint Eigenvalue Problems with Arbitrary Spectrum

U. Mertins[1]

(1) Technische Universität Clausthal, Clausthal-Zellerfeld, Germany

It was shown recently in [13] that the Goerisch method provides upper and lower bounds to eigenvalues of variationally posed self-adjoint eigenvalue problems with arbitrary spectrum. In the present paper the approximation of eigenelements is established. In addition, the convergence of the eigenvalue and eigenelement approximations is shown in a pure func-tional analytic procedure. A numerical example is given where the curve veering phenomenon occurs.

Keywords: Eigenvalue problems, variational methods, upper and lower bounds to eigenvalues, approximation of eigenelements, convergence of the Goerisch method, curve veering

Mertins U.: On the Convergence of the Goerisch Method for Self-Adjoint Eigenvalue Problems with Arbitrary Spectrum. Z. Anal. Anwend. 15 (1996), 661-686. doi: 10.4171/ZAA/722