Iterative thresholding low-rank time integration for high-dimensional problems

Abstract

This work analyzes a method for time integration of high-dimensional linear Schr\"odinger-type problems based on hierarchical tensor approximations. In particular, this method provides a balance between error bounds and associated approximation ranks, using a scheme for iterative refinement with soft thresholding of tensors. The practical performance of the method is illustrated by numerical tests on coupled oscillators.