Combine aggressive compression with operator recycling

Determine how aggressive low-rank compression can be combined with operator recycling in iterative methods for repeated tensor-train matrix–vector products.

Background

The paper develops a pre-sketched streaming tensor-train approximation strategy that absorbs randomized sketches into the cores of a tensor-train operator. This absorbed, sketched operator can be reused when the same operator is applied repeatedly, particularly in iterative methods such as power and Krylov methods.

The paper also investigates repeated operator applications with rank growth between truncations and finds experimentally that allowing ranks to grow before sharp truncation is advantageous only in limited settings. The unresolved issue is how to exploit operator recycling together with more aggressive compression in iterative methods, beyond the tested strategies and regimes.