Output bounds for reduced-basis approximations of symmetric positive definite eigenvalue problemsOutput bounds for reduced-basis approximations of symmetric positive definite eigenvalue problems Peer-Reviewed Journal Publication Δημοσίευση σε Περιοδικό με Κριτές 2015-10-172000enWe 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.http://creativecommons.org/licenses/by/4.0/Comptes rendus de l'Academie des sciences. La vie des sciences2331153–158 Rovas Dimitrios Ροβας Δημητριος Pateras, Anthony, 1979- Ivan B. Oliveira Maday, Yvon, 1957- Luc Machiels Elsevier Greek mathematics mathematics greek greek mathematics