Speaker
Description
We present a new technique for efficiently compressing matrix–vector products in the tensor-train (TT) format, avoiding the explicit formation of intermediate tensors arising from standard MPO–MPS multiplication. The proposed method performs the compression in a single pass, leading to significant computational and memory savings.
From a theoretical point of view, the resulting approximation is mathematically equivalent to the streaming tensor-train approximation introduced by Kressner, Vandereycken, and Voorhaar. However, our approach admits a more efficient implementation, tailored to the structure of TT operators and vectors, and better suited for large-scale and iterative computations.
Beyond accelerating the fundamental MPO–MPS product, the new method allows us to produce a compressed representation of the operator that can be computed once and reused across multiple applications. This feature is particularly advantageous in iterative algorithms where the same operator is applied repeatedly. We demonstrate how this leads to substantial speedups in Krylov subspace methods, with a special focus on the synergy between the proposed technique and sketched GMRES.