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 ...

We propose a new algorithm for solving the semiclassical time–dependent Schr¨odinger equation. The algorithm is based on semiclassical wavepackets. Convergence is proved to be quadratic in the time step and linear in the semiclassical parameter !. To the the authors’ best knowledge, all earlier algorithms had errors that grew as the semiclassical parameter was decreased.

Private set operations allow correlation of sensitive data from multiple data owners. Although intensely researched, current solutions still exhibit limited scalability in terms of the supported maximum set size and number of sets. To address these issues, we propose a new approach to private set operations based on a combination of efficient secure multiparty computation and bloom filters, a space-efficient probabilistic data structure ...