On low-rank approximability of solutions to high-dimensional operator equations and eigenvalue problems

Understand

Low-rank tensor approximation techniques attempt to mitigate the overwhelming complexity of linear algebra tasks arising from high-dimensional applications.

• In this work, we study the low-rank approximability of solutions to linear systems and eigenvalue problems on Hilbert spaces.
• Although this question is central to the success of all existing solvers based on low-rank tensor techniques, very few of the results available so far allow to draw meaningful conclusions for higher dimensions.
• In this work, we develop a constructive framework to study low-rank approximability.