Section: New Results

Application of greedy algorithms

Participants : Sébastien Boyaval, Eric Cancès, Virginie Ehrlacher, Tony Lelièvre.

Greedy algorithms are used in many contexts for the approximation of high-dimensional functions: Proper Generalized Decomposition, Reduced Basis techniques, etc.

Various greedy algorithms for high-dimensional non-symmetric problems, and inherent theoretical and practical difficulties have been analyzed in [52] . Current research now aims at extending these techniques to the approximation of high-dimensional spectral problems. Prototypical applications include electronic structure calculations or the computation of buckling modes in mechanics.

In probabilistic methods for uncertainty quantification in mechanics, S. Boyaval has used a greedy algorithm to construct control variates for accelerating Monte-Carlo simuation in the cases where an expectation has to be computed many times [21] . The work is being applied to the uncertainty quantification in numerical models for hydraulic engineering.

Finally, in [55] , Fabien Casenave (CERMICS), Alexandre Ern (CERMICS) and Tony Lelièvre study the influence of round-off errors on the evaluation of the a posteriori estimators in the reduced basis approach. In practice, the evaluation of the error estimator can become very sensitive to round-off errors. An explanation of this fact is proposed, as well as efficient remedies.