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Institutional Repository [SANDBOX]
Technical University of Crete
Technical University of Crete
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| URI: | http://purl.tuc.gr/dl/dias/A3F5A8EC-A6F5-458E-BE8F-E9E1737BCD33 | ||
| Year | 2000 | ||
| Type of Item | Peer-Reviewed Journal Publication | ||
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| Bibliographic Citation | L. Machiels, Y. Maday, I.B. Oliveira, A.T. Patera, D.V. Rovas ,"Output bounds for reduced-basis approximations of symmetric positive definite eigenvalue problems." Comp. Rendus de l'Acad. des Sc.Series I-Math.,vol. 331 ,no.2 ,pp.153-158,2000.doi:10.1016/S0764-4442(00)00270-6 https://doi.org/10.1016/S0764-4442(00)00270-6 | ||
| Appears in Collections |
We propose a new reduced-basis output bound method for the symmetric eigenvalue problem. The numerical procedure consists of two stages: the pre-processing stage, in which the reduced basis and associated functions are computed—“off-line”—at a prescribed set of points in parameter space; and the real-time stage, in which the approximate output of interest and corresponding rigorous error bounds are computed—“on-line”—for any new parameter value of interest. The real time calculation is very inexpensive as it requires only the solution or evaluation of very small systems. We introduce the procedure; prove the asymptotic bounding properties and optimal convergence rate of the error estimator; discuss computational considerations; and, finally, present corroborating numerical results.
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