The present paper is concerned with the study of manifold-valued multiscale transforms with a focus on the Stiefel manifold. For this specific geometry we derive several formulas and algorithms for the computation of geometric means which will later enable us to construct multiscale transforms of wavelet type. As an application we study compression of piecewise smooth families of low-rank matrices both for synthetic data and also real-world ...

The nonlinear spatially homogeneous integro-differential Boltzmann equation is a uniquely challenging task for numerical solvers due to the difficulty of efficiently computing the collision operator. A popular method is to expand the solution in Fourier modes and to truncate the collision operator. We present an approach based on the hyperbolic cross, whereby the performance can be greatly enhanced in some situations, as well as an offset ...