Comparison of Errors in Upper and Lower Bounds to Eigenvalues of Self-Adjoint Eigenvalue Problems |
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Authors: | Sabine Zimmermann |
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Institution: | Fachbereich Mathematik , Technische Hochschule Darmstadt , Schlofigartenstrafle 7, Darmstadt, Bundesrepublik, W-6100, Deutschland |
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Abstract: | The error in lower Lehmann bounds to eigenvalues of self-adjoint problems is estimated from above by a constant multiple of the error in corresponding, upper Rayleigh-Ritz bounds. The constant involved is explicitly computable and monotonicallydecreasing in the dimension of the approximate eigenvalue problems. Asymptotically, the same inequality holds for the general Lehmann-Goerisch approach. Numerical examples are included in order to investigate the accordance of computed error quotients and theoretical bounds. |
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Keywords: | 65J10 65N25 49R05 34L15 35P15 Mathematics Subject Classification (1991) |
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