A sparse multiresolution stochastic approximation for uncertainty quantification (Q2869180)

The paper gives a multiresolution approach on sparse multiwavelet expansions for uncertainty propagation. The efficiency of the compressive sampling method in recovering stochastic functions having sparse expansions in multiwavelet bases is proved and then used in obtaining the main results. In order to improve convergence rates of approximating responses exhibiting sharp gradients or discontinuities, an adaptive importance sampling strategy is applied. Various sampling strategies are considered, too. The convergence of the method is demonstrated by an application to a rotated version of the Kraichnan-Orszag problem with random initial conditions.NEWLINENEWLINEFor the entire collection see [Zbl 1264.65002].