Parallel Algorithms for Tensor Train Arithmetic

Understand

We present efficient and scalable parallel algorithms for performing mathematical operations for low-rank tensors represented in the tensor train (TT) format.

• We consider algorithms for addition, elementwise multiplication, computing norms and inner products, orthogonalization, and rounding (rank truncation).
• These are the kernel operations for applications such as iterative Krylov solvers that exploit the TT structure.
• The parallel algorithms are designed for distributed-memory computation, and we use a data distribution and strategy that parallelizes computations for individual cores within the TT format.