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Efficient greedy algorithms for high-dimensional parameter spaces with applications to empirical interpolation and reduced basis methods

Jan S. Hesthaven, Benjamin Stamm, Shun Zhang (2014)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We propose two new algorithms to improve greedy sampling of high-dimensional functions. While the techniques have a substantial degree of generality, we frame the discussion in the context of methods for empirical interpolation and the development of reduced basis techniques for high-dimensional parametrized functions. The first algorithm, based on a saturation assumption of the error in the greedy algorithm, is shown to result in a significant reduction of the workload over the standard greedy...

Eigenvalues in the large sieve inequality, II

Olivier Ramaré (2010)

Journal de Théorie des Nombres de Bordeaux

We explore numerically the eigenvalues of the hermitian form ∑ q ≤ Q ∑ a mod * q ∑ n ≤ N ϕ n e ( n a / q ) 2 when N = ∑ q ≤ Q φ ( q ) . We improve on the existing upper bound, and produce a (conjectural) plot of the asymptotic distribution of its eigenvalues by exploiting fairly extensive computations. The main outcome is that this asymptotic density most probably exists but is not continuous with respect to the Lebesgue measure.

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