arXiv subjects

Polina Sachsenmaier

Publications and source records attributed to Polina Sachsenmaier.

2 recordsLinked to original sources

arXiv2026

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

This work analyzes a method for time integration of high-dimensional linear Schrödinger-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.

math.NA↗

arXiv2025

Iterative thresholding low-rank time integration

We develop time integration methods in low-rank representation that can adaptively adjust approximation ranks to achieve a prescribed accuracy, while ensuring that these ranks remain proportional to the corresponding best approximation ranks. Our approach relies on an iterative scheme combined with soft thresholding of the iterates. A model case of a time-dependent Schrödinger equation with low-rank matrix approximation is analyzed in detail, and the required modifications for second-order parabolic problems are described. Numerical tests illustrate the results for both cases.

math.NA↗